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?

avamarie Apr 7, 2020

#1**+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!

HELPMEEEEEEEEEEEEE Apr 7, 2020

#2**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

CPhill Apr 7, 2020

#3**+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!! **

KingHTML Apr 7, 2020