Suppose we use x to represent the width of the rectangle in feet. The equation for the area of the rectangle can be written as

66 = x(2x+1)

2x^2 + x - 66 = 0 (subtract 66, put in standard form)

x = (-1 ± √(1^2 - 4(2)(-66)))/(2(2)) (use the quadratic formula)

x = (-1 ± √529)/4 (simplify)

x = (-1 ± 23)/4 (simplify)

x = {-6, 11/2} (find the two solutions)

Only the positive solution makes sense as a dimension.

66 = x(2x+1)

2x^2 + x - 66 = 0 (subtract 66, put in standard form)

x = (-1 ± √(1^2 - 4(2)(-66)))/(2(2)) (use the quadratic formula)

x = (-1 ± √529)/4 (simplify)

x = (-1 ± 23)/4 (simplify)

x = {-6, 11/2} (find the two solutions)

Only the positive solution makes sense as a dimension.

**The width (x) is 5.5 ft; the length (2x+1) is 12 ft**.