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A square and a right triangle have equal perimeters. The legs of the right triangle 20 in. and 15 in. What is the area of the square, in square inches?

Apr 7, 2020

#1
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If the legs of the right triangle are 20 and 15, we know it's in the ratio 3:4:5 meaning the hypotenuse is 25. That makes the perimeter of the triangle 60 inches. If the triangle and square have the same perimeter, then 60/4= 15 inches giving us the side length of the square. The area of a square is its side length squared which is 15^2= 225 in^2.

Hope it helps!

Apr 7, 2020
#2
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The hypotenuse of the right triangle  = sqrt  [ 20^2 + 15^2] = sqrt [ 400 + 225]  = sqrt [ 625]   = 25

So....the perimeter of the triangle is  15 + 20 + 25  =   60  in

Then....the side of the square =  60 / 4  =   15  in

And the area of the square  =   side^2  =  15^2  =  225 in^2   Apr 7, 2020
#3
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Since the legs of the right triangle are 20 and 15, we can use the Pythagorean Theorem to find the hypotenuse which is the other side.

a^2 + b^2 = c^2

15^2 + 20^2  = c^2

225 + 400 = c^2

625 = c^2

c = 25

Therefore, the hypotenuse of the right triangle or the final side is 25, now we can find the sum of the sides of the right triangle.

25 + 20 + 15 = 60

Since the square and right triangle have equal perimeters the square's perimeter has to be 60 too!

4a = 60

a = 15

One of the square's sides is 15, and it's area is simply side squared, which is 15^2 and that is 225.

Enjoy!! 