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.