The length of a rectangle is 3 ft more than twice the width, and the area of the rectangle is 77 ft2 . Find the dimensions of the rectangle.

Let L represent length     W represent width     and     A represent area.

Since the length is 3 ft more than twice the width, we can write this as     L = 3 + 2W

The formula for the area of a rectangle is     A = L x W

Since the area is 77,     77  =  L x W

Substituting:               77  =  (3 + 2W) x W

Multiplying out:           77  =  3W + 2W²

Rewriting:                  2W² + 3W  =  77

Subtracting:               2W² + 3W - 77  =  0

Factoring:                   (2W - 11)(W + 7)  =  0

So, either  2W - 11 = 0   --->  2W  =  11   --->   W = 5.5 ft

           or  W + 7  =  0   --->   W  =  -7    (not possible)

Since  L  =  3 + 2W   --->   L  =  3 + 2(5.5)  =  14 ft