A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square.

Are you sure it is a square and not a rectangle...

Side of the square =

(product of the leg lengths) / ( sum of leg lengths) =

[ 1 * 3 ] / [ 1 + 3] =

3/4

Area = (3/4)^2 = 9/16