The length of a rectangle is 1 ft less than double the width, and the area of the rectangle is 21 ft^2. Find the dimensions of the rectangle.

Let the width be w, then length = 2w - 1

Area = length times width = w (2w - 1) = 21.

Thus, 2w^2 - w = 21 or 2w^2 - w - 21 = 0

Solving the quadratic equation gives that w = 3.5.

Therefore, width is 3.5 ft and length is 2 (3.5) - 1 = 6 ft.