WEBVTT
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for the kind to be made From six pieces of
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wood. The four exterior pieces have been cut with
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the lens indicated in the figure. Mhm. Right
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. So these are the four exterior pieces we are
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talking about. That is A A. And B
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. B. Right? So it is us that
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these are cut in with the lens indicated in the
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figure to maximize the area of the kite. How
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long should the diagonal pieces speak? Right. So
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we need to find the length of diagnosed A.
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C. We have supposed let us say this is
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A. B. C. D. Right?
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For a guide. Now we have supposed X.
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X. Here this is X. Let us say
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this is why. And this is it. Right
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. So this becomes very simple now, so we
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need to find the length of time, signal A
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. C. And needed to maximize the area.
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So let us see how do we do So?
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So Here the length of the site is given that
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it's 80 A. D. A B. That
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is A D. A B are equal given that
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is A and B. C. Do you see
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is given to us that is B. Small B
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. And we have supposed Bte equals two. B
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. D. Is if it is accident, it
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will be also if that becomes towards right. So
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now A C. Is equal to Q. Z
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equals two. Let's just say it is, can
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we request to buy places like. Alright, so
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now this is for sure that a small A.
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That this side A is less than I remember this
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. So this is very important. Alright. So
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now on applying pythagoras students to do the right angle
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triangle a soda. Can we do So yes.
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So this is let us say this is O.
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A. O. D. Is the right angle
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triangle. So in this we will apply the path
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of a restaurant. We will get 80s where that
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is our high port news. Right? So it
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is squared equals to a oh a square plus or
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D squared. That that implies a square. That
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this small A square as it was two Y squared
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plus X squared. So I will be in terms
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of a what will it will be, it will
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be one. So we will take all these values
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in towns off a right we will try to.
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So unlike uh in terms of A. And next
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year right A B. And X. Here see
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Okay so it will find further value of said then
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it will be also in terms of A B C
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A B X only. Right? So that it
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becomes very simple. Now we will apply this category
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stare um to the right angle triangle again, O
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C. D. Again. So O. C
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. D jane. So here it becomes serious square
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. That is high partners. A city here.
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And this is a right angled triangle already. So
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this becomes city squared equals two Oc square. This
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or the square. So this will give us a
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small B squared equals C squared the sexes square.
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So in terms of being next we will get that
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. It was too be square root over B squared
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minus Access world. So these are the equation one
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. And we have supposed great. So, because
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why we are doing so well into because why place
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that we need to find here. That is why
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place it is nothing. But that is easy.
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And we need to find a mandatory. So that's
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why we are doing so. Right? So now
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on the length of the diagonal, A C.
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Is equal to Q. That is my place there
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. So this will give us from equation to one
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and two. We will put the value for buying
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there in terms of A X. N. B
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. Right? So this will become Q equals to
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that is length of the diagonal eight. It was
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too wrote over a square minus X squared less route
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over B squared minus X squared. So the diagonal
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BD is equals true. B Is the question to
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works. Yes, because BD BD is here explicit
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. That makes two weeks. Right? So this
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will be representatives be here. Right? So now
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we will just write the area of the kite of
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the diagnosed baby. Right? Except okay, So
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this will be this will be nothing. But the
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area will be uh area will be lent half into
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base in too high. Great. So happened to
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base into hiatus. Happened to be D into B
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. D. Into a C. Right? So
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that is Bds represented by P. And S is
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represented by cuba. Remember this. So we will
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just put all the values we have calculated above.
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We can just write the value of P Q.
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Right? So when we will solve for a that
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is the function of x ray a square and be
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A and B are constant here. Great. So
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we are calculating here. So area becomes X into
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route over a squared minus X squared plus wrote over
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this where minors access. Right? So we know
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this is very important formula. Next step is to
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maximize the area of kind. So we know that
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to maximize anything. We just differentiate that value and
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put that equals to zero. So we will get
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the maximum value. So this is very important and
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very common thing. We do indeed mathematics. Right
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? So here it well differentiated and differentiate shared the
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area because we want to maximize the area. So
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we will just get the value of this. You
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can say this value of X. So that the
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area will be maximum. So that is what we
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need to find it. Yes, so a dash
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X is equal to zero. Now we will differentiate
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the value. So after differentiation we will finally get
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the equation route over a square minus x squared plus
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route over b squared minus x squared that will be
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into one minus access choir by route over a squared
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minus x squared room moment be square minus x squared
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That will give us. So These are the two
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or two factors you can say yes we have factories
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did. So this value should be close to zero
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as well as this value should be then we'll see
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which one should be correct. one of this will
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be around and another one week. Right so let
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us right for the first part that is route over
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a square minus X squared plus route over b squared
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minus x squared because 20 when we'll put in this
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way so the a squared plus a squared becomes sequence
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two piece which is not correct. Thanks because we
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have a zoom a is less than the right now
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let's see for the second part that is one minus
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x squared by a route over a square minus X
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squared into route over these were minus access. So
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then well then we will do equals to zero.
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We will get this value right we will solve for
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the situation. After solving the situation. After going
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through steps we'll get something which is equal to route
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over you can say a square this is a square
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I'm sorry of route over a square minus x squared
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into route over b squared minus X squared equals two
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here, excess spread. So we will just square
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this both sides we will get this extra power for
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here. In the right hand side After solving with
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all that steps this extra power. Extra power gets
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canceled. Extra powerful and extremely powerful from the left
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hand side to write and say it gets cancelled date
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. So no, what else could be done now
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here the equation finally becomes is a squared b squared
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00:10:09.929 --> 00:10:15.429 A:middle L:90%
minus a squared X squared minus b squared x squared
150
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equals to zero. Right? So when we will
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solve for it We will get x equals two route
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over a square. Be square upon a square.
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Let's be spread. Okay, so this is it
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person. Right. So finally we will get the
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value of X. That is X. Is equal
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to a B divided by ruled over a squared plus
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B squared. So this is one. Right?
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So for two weeks but he is nothing but length
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of dying diagnoses. Remember this length of the diagnosis
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VD that is peace. It was two weeks that
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is to into two MB. You can see the
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wavy by a square. Let's be spread it really
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Right. So we have got this finally and therefore
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bidding. Right. So this is our first answer
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. No, we will calculate for diagonal. Yes
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. Right. So now for diagonal A C.
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We will write Q equals to wipe this said and
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we know by the value of finds it. Now
169
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we will put now we know we also know the
170
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value of X. Right? We have calculated above
171
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. So we will put that value yes. From
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the equation you can see film equation four equation Yes
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four. Right. So now yeah what will be
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the further steps we will solve for this equation.
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We will be getting here a to the power phone
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. Let us say to the power for divided by
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route over. Not not recover. It will be
178
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square. So square square will be the square root
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and a square A square root square off the square
180
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root will be Same. Only Baba is 1 1
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. Right? So here is squared plus b squared
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. This is rude. Over 88 to the power
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four divided by a squared plus B squared plus wrote
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over. All right over B to the powerful upon
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a square Plys who spread. Okay, okay.
186
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Is it the same? Yes. So now it
187
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becomes a Squire divided by suit over is square plan
188
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B square close B squared divided by route over is
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purpose. This Right. So this finally gives us
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the bad news that is going to work a square
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piece. So this is nothing. But this is
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a time length of diagonal. Easy so length of
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guidance. Easy. Right. So this is also
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a final answer. We have got the value 40BT
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as well as a C to maximize the area.
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I hope your industrial the concept. Thank you for
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watching. Mm hmm.