Question

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

Answer 1

225
`in^(2)`

Explanation:

First, find the perimeter of the triangle. We will use the Pythagorean Theorem to find the length of the hypotenuse of the triangle.

`a^(2)` +
`b^(2)` =
`c^(2)`

`20^(2)` +
`15^(2)` =
`c^(2)`

400 + 225 =
`c^(2)`

625 =
`c^(2)`

`√(625)` =
`\sqrt{c^(2) }`

25 = c

The perimeter of the triangle is: 25 + 20 + 15 = 60

The perimeter of the square is the same (60), so the length of each side is 15 (60/4).

To find the area of a square you multiply the length times the width, or in this case, 15 x 15 which is 225.

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