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?
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!
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
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.
225 square inches