22) A square and rectangle have equal areas. The length of the rectangle is five inches more than twice the side of the square. The width of the rectangle is 6 inches less than the side of the square. Find the length of the side of the square.

Here two areas are equal: That of the square equals that of the rectangle.

Let s represent the side length of the square. Then the area of the square is s^2.

The length of the rect. is 2s+5, and the width of the rect. is s-6.

" A square and rectangle have equal areas."

Thus, s^2 = (2s+5) (s-6), or s^2 = 2s^2 - 12s + 5s - 30

Simplifying, 0 = s^2 - 7s - 30. This factors to 0 = (s-10) (s+3).

Thus, s may be either 10 or - 3. Lengths are not negative, so omit the - 3. The side of the square, s, is 10 units.

Then the width of the rect. is s-6 = 4, and the length of the rect. is 2s+5, or 2 (10) + 5, or 25.