Answer:
Length: 5 ft; width: 4 ft.
Step-by-step explanation:
A = LW     formula for area of rectangle
(2x + 1)(2x) = 20      substitute length, width, and area into formula
4x² + 2x - 20 = 0      use the distributive property to multiply out left side
2x² + x - 10 = 0         divide both sides of equation by 2
(2x + 5)(x - 2) = 0        factor out trinomial
2x + 5 = 0  or  x - 2 = 0        use zero product rule to solve for x
2x = -5  or x = 2       subtract 5 from both sides; add 2 to both sides
x = -5/2  or  x = 2
We discard x = -5/2 since it would give negative length and width, and the length and width cannot be negative.
Length: 2x + 1 = 2(2) + 1 = 5
Width: 2x = 2(2) = 4
Length: 5 ft; width: 4 ft.