Step-by-step explanation:

GIVEN:

Area = A = 132 ft²

Width = W

Length = L = 2 feet less than 4 times the width

L = 4W - w

FORMULA FOR AREA OF A RECTANGLE:

L × w = A

• Substitute given dimensions

(4w -2)(w) = 132

• Distribute w

4w² -2w = 132

4(w² - (2/4)w) = 132

• Divide both sides of equation by 4

4(w² - (2/4)w)/4 = 132/4

w² - (2/4)w = 33

• By completing the square

w² - (1/2)w + 1/16 = 33 + 1/16

• The left side is now a perfect square

(w - 1/4)² = 529/16

• Take the square root of both sides of equation

√(w - 1/4)² = ±√(529/16)

w - 1/4 = ±23/4

ROOT 1:

w - 1/4 = 23/4

w - 1/4 + 1/4 = 23/4 + 1/4

w = 6 ft

ROOT 2:

w - 1/4 = -23/4

w - 1/4 + 1/4 = -23/4 + 1/4

w = -11/2 ft

NOTE: Since we are talking about dimension, neglect the negative root. Because there is no such thing as negative length and width.

• Substitute value of width to the original equation

L × w = A

(L × w)/w = A/w

L = A/w

L = 132 ft²/6 ft

L = 22 ft

The length of the rectangle is 22 ft while its width is 6 ft.