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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
avatar+932 
+1

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
avatar+111329 
0

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

 

 

cool cool cool

 Apr 7, 2020
 #3
avatar+50 
+2

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. 

 

Answer: 

225 square inches

 

Enjoy!! smiley

 Apr 7, 2020

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