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?
The legs of the right triangle are in a $3:4$ ratio, so the right triangle is similar to a $3 - 4 - 5$ right triangle and thus it has hypotenuse $5\cdot 5 = 25$.  The perimeter of the right triangle is then $15 + 20 + 25 = 60$.  Then the square has side length $60/4=15$ and area $15^2 = \boxed{225}$ square inches.