The area of a rectangle is 63 ft^2, and the length of the rectangle is 11 ft more than twice the width. Find the dimensions of the rectangle.

Let width = x

Let length = 2x + 11

Area = 63 ft2

length × width = Area

x(2x + 11) = 63

2x2 + 11x = 63

Subtract 63 on both sides of equation.

2x2 + 11x - 63 = 0

Factor the left side of equation.

(2x - 7)(x + 9) = 0

x = 7/2 and x = -9

Since the dimensions cannot be negative, we accept the positive value of x:   x=7/2.  Substitute this value of x into the dimensions

width = 3.5 ft

length = 2(3.5) + 11 = 7 + 11 = 18 ft