3. The perimeter of a rectangle is 22 inches, and the area is 28 square inches.  What is the product of the lengths of the diagonals, in square inches?

The length of each diagonal is  by the Pythagorean Theorem.

The perimeter of the rectangle is , and the area is .

By simplifying and substituting, we get

Factoring, 

If

Each diagonal is  so the product of the lengths is 65.