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Let's do this question, the square below has been divided into four rectangles, the area of two of

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the rectangles is given if the length of each of the segments in the diagram is an integer, what is

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the area of the original square?

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But this is a very good question because the video give it a thought and then let's do it together.

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All right.

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We're back.

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I hope you have given it a thought.

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Let's do it together.

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The first thing that you need to notice over here is this measurement is given in Meter Square and this

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measurement is given in Centimeter Square.

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But you need to convert them either both into centimeters square or both into meter square to proceed.

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So let's see how to do that.

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So we know that hundred in two hundred centimeter square is equal to one meter square.

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Why is that so?

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That's because hundred centimeter is equal to one meter.

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So what is standard in two hundred centimeter square?

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Let me write it like this.

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Let's start with one meter square, so one meter square is the same as one meter into one meter.

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Right now instead of one meter, I can write hundreds and.

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So that's equal to a hundred centimeter in two hundred centimeters.

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That is why we say that one meter square is equal to under two hundred centimeters square.

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All right, let's proceed.

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Having established this, let's try to convert three six zero zero zero zero centimeter square into

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metre square, not to do that, we just need to divide this by Hundert in two hundred.

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Right.

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But over here, you can see one centimetre square from this equation.

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You can see one centimetre square is equal to one divided by another in two hundred meter square right

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now.

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Therefore these many centimetres square that is three, six or by four zeros, centimetres square will

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be equal to this much.

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Multiplied with this value over here.

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So that's how we get this part over here.

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Let me make some space.

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All right, so if you solve this equation, you will see that this is equal to thirty six metre square

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for this area over here is 36 meter square and this is twenty four meters square.

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All right, let's proceed.

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So we have converted this into Meter Square.

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Now over here, it's given that this shape is a square, right.

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Therefore we can conclude that a policy is equal to B plus B because sides of a square are equal to

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A plus is equal to B plus.

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These sides are equal and it is given that.

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This area into B is equal to twenty four meter square, right, and it is given that scene today is

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equal to thirty six meter square.

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But let's write that over here into these twenty four meter square and seen today is equal to thirty

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six meter square.

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Now we need to find these sites.

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What are the possibilities.

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Where you get in to be is equal to twenty four.

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Let's write all the possibilities.

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I can have one in the 24, two in the 12, three into it or into six, right.

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The next one would be six in the four.

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And that's a repetition of this.

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So I don't count it over here.

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And remember, why did I write it like this from the figure?

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You can see that B is greater than A right to be written in the manner that B were here is greater than

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it.

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All right.

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Now, what are the possibilities for seeing today is equal to thirty six.

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Let's write all the possibilities.

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You have one in the six to into eighteen three in the 12, 14 to nine and six into six.

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And you stop at this point.

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Now over here you can see C is greater than the right.

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So that's why we have written it in this manner.

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And remember, it's given in the question that the length of each segments in the diagram is an integer,

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but that's why we don't take, for example, five into twenty four by five that does twenty four by

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five does not give an integer, for example.

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All right.

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Now, having established this much, we need to find the value of A, B, C and D so that we can get

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the side of the square.

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And if we can get the side of the square we can find the area of the square.

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Now, one way would be to try all of these combinations, but that is take too much time digging and

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that is not the optimal way.

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Let's proceed over here.

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We know that a policy is equal to B plus B right now.

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From this, I can understand that B minus.

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There has to be equal to C minus B right now is that we had to have B, I take it, to the side.

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So that becomes B minus eight and I take these to the side.

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So that becomes C minus the the these two have to be equal.

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So let me find B minus in all these cases.

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So over here, B's twenty four is one, so B minus is twenty four.

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Minus one.

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That's twenty three.

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What about here.

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That's twelve minus two.

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That gives me ten.

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Eight minus three is five and six.

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Minus four is too.

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What about these cases.

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Thirty six minus one.

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That's C minus the right now does X minus one is thirty five.

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Eighteen minus two is sixteen.

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Twelve minus three is nine.

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Nine minus four is five and six minus six is zero.

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Now these two have to be equal.

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Right.

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So can you find out in which case it's equal or here you have five and over here you have five.

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So it has to be three, B has to be eight, B has to be four, and C has to be nine.

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Now we know that the side of the square is a policy that would be three plus nine and that gives you

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twelve.

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Therefore, if the site is twelve, we know that area of a square is a square and therefore the area

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is equal to Twelve Square, which is equal to one forty four.