Square BCFE is inscribed in right triangle AGD, as shown below. If AB = 28 units and CD = 56 units, what is the area of square BCFE?
Let S be the side of the square
Note that triangle ABE is similar to triangle FCD
So
AB/ EB = FC / CD
28/ S = S / 56 cross-multiply
S^2 = 28 * 56 = 1568 = area of square BCFE
