Let's do this question, the square below has been divided into four rectangles, the area of two of
the rectangles is given if the length of each of the segments in the diagram is an integer, what is
the area of the original square?
But this is a very good question because the video give it a thought and then let's do it together.
All right.
We're back.
I hope you have given it a thought.
Let's do it together.
The first thing that you need to notice over here is this measurement is given in Meter Square and this
measurement is given in Centimeter Square.
But you need to convert them either both into centimeters square or both into meter square to proceed.
So let's see how to do that.
So we know that hundred in two hundred centimeter square is equal to one meter square.
Why is that so?
That's because hundred centimeter is equal to one meter.
So what is standard in two hundred centimeter square?
Let me write it like this.
Let's start with one meter square, so one meter square is the same as one meter into one meter.
Right now instead of one meter, I can write hundreds and.
So that's equal to a hundred centimeter in two hundred centimeters.
That is why we say that one meter square is equal to under two hundred centimeters square.
All right, let's proceed.
Having established this, let's try to convert three six zero zero zero zero centimeter square into
metre square, not to do that, we just need to divide this by Hundert in two hundred.
Right.
But over here, you can see one centimetre square from this equation.
You can see one centimetre square is equal to one divided by another in two hundred meter square right
now.
Therefore these many centimetres square that is three, six or by four zeros, centimetres square will
be equal to this much.
Multiplied with this value over here.
So that's how we get this part over here.
Let me make some space.
All right, so if you solve this equation, you will see that this is equal to thirty six metre square
for this area over here is 36 meter square and this is twenty four meters square.
All right, let's proceed.
So we have converted this into Meter Square.
Now over here, it's given that this shape is a square, right.
Therefore we can conclude that a policy is equal to B plus B because sides of a square are equal to
A plus is equal to B plus.
These sides are equal and it is given that.
This area into B is equal to twenty four meter square, right, and it is given that scene today is
equal to thirty six meter square.
But let's write that over here into these twenty four meter square and seen today is equal to thirty
six meter square.
Now we need to find these sites.
What are the possibilities.
Where you get in to be is equal to twenty four.
Let's write all the possibilities.
I can have one in the 24, two in the 12, three into it or into six, right.
The next one would be six in the four.
And that's a repetition of this.
So I don't count it over here.
And remember, why did I write it like this from the figure?
You can see that B is greater than A right to be written in the manner that B were here is greater than
it.
All right.
Now, what are the possibilities for seeing today is equal to thirty six.
Let's write all the possibilities.
You have one in the six to into eighteen three in the 12, 14 to nine and six into six.
And you stop at this point.
Now over here you can see C is greater than the right.
So that's why we have written it in this manner.
And remember, it's given in the question that the length of each segments in the diagram is an integer,
but that's why we don't take, for example, five into twenty four by five that does twenty four by
five does not give an integer, for example.
All right.
Now, having established this much, we need to find the value of A, B, C and D so that we can get
the side of the square.
And if we can get the side of the square we can find the area of the square.
Now, one way would be to try all of these combinations, but that is take too much time digging and
that is not the optimal way.
Let's proceed over here.
We know that a policy is equal to B plus B right now.
From this, I can understand that B minus.
There has to be equal to C minus B right now is that we had to have B, I take it, to the side.
So that becomes B minus eight and I take these to the side.
So that becomes C minus the the these two have to be equal.
So let me find B minus in all these cases.
So over here, B's twenty four is one, so B minus is twenty four.
Minus one.
That's twenty three.
What about here.
That's twelve minus two.
That gives me ten.
Eight minus three is five and six.
Minus four is too.
What about these cases.
Thirty six minus one.
That's C minus the right now does X minus one is thirty five.
Eighteen minus two is sixteen.
Twelve minus three is nine.
Nine minus four is five and six minus six is zero.
Now these two have to be equal.
Right.
So can you find out in which case it's equal or here you have five and over here you have five.
So it has to be three, B has to be eight, B has to be four, and C has to be nine.
Now we know that the side of the square is a policy that would be three plus nine and that gives you
twelve.
Therefore, if the site is twelve, we know that area of a square is a square and therefore the area
is equal to Twelve Square, which is equal to one forty four.