Let's do this question, Esquire is inscribed in a circle of cites 13, 15 and four centimetre.
One of the sides of the square lies on the longest side of the triangle.
The other two vertices of the square, that's the other side of the triangle.
Find the length of the square.
All right.
Pause the video, give it a try and then let's do it together.
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We are back.
Let's do it together.
Over here.
I have my triangle and it's mentioned that the square is placed.
That's that it's one side is on the longest side of the triangle.
So let's mark the sides and the partisans of the triangle.
Now, this has to be 15.
That is the longest side.
And let's take this as 13.
And this has four at these points, B, ABC.
Now let's mark the citizens of the square as P.
Q are and s now we need to find the length of the square right now.
What is the same perimeter of this triangle that would be 15 plus four plus thirteen by two, which
is equal to sixteen.
Now we know how to find the area of a triangle if you know the three sites as.
But heroin's formula.
Right.
That would be square root of S in S minus in the S minus B into S minus C.
Right.
So let's apply that over here.
You get the area as.
Square root of sixteen into one, into 12 into three, that is equal to twenty four to the area of triangle,
ABC is equal to twenty four.
All right, now let me draw a perpendicular to Vertex eight.
So that's the altitude.
And let me take that as it's the area also can be found as 15 in to it's by two.
Right, because it is half into base, into height.
Now this has to be equal to twenty four.
So let me get this to twenty four and I get that the height that is edge over here will be equal to
16 by five.
All right.
Now let this height over here be êtes to.
That is the height of a barbecue.
All right, so let this be it, too.
Now you can see that triangle ABC and Triangle EPICA, that is this smaller triangle and this big triangle
are similar, right?
Why is that so?
Because this angle will be equal to this angle.
This angle will be equal to this angle over here right now.
Why is that so?
Can you tell me why that is?
We know that this side is parallel to the side because this is a square, right.
So this angle over here has to be equal to this angle because this side is lying on ABC.
That means BQ is parallel to ABC.
Therefore, these two angles are corresponding angles.
Similarly, this angle on this angle are also corresponding angles.
That's why Triangle ABC is similar to triangle apical Asper aerial.
All right.
So these two.
Angles are equal and we have these two angles as equal.
All right, now over here, this angle is a common angle right now because these two triangles are similar.
We can say that it's too divided by eight is equal to a divided by B.C. Right now, I'm taking the side
of the square as two to sword to divide it by.
It is equal to a divided by B.C..
Now we know that.
It's too can be written as 16 by five minus eight, right?
Why is that so?
Six by five is it?
And this land over here will be equal to it because this is a square.
Right.
So therefore, it's two has to be 16 by five minus eight.
Right.
So let's right that over here, 16 by five minus eight divided by 16 by five, which is which is equal
to a by 15.
Right.
Because equal to 15.
Now over here, let's solve for it.
We get sixteen minus five by sixteen is equal to about 15 or we get ninety one is equal to 240 or is
equal to 240 by ninety one.
And that is the answer to this question because we have to find the length of the square.