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!!