Question

A rectangle has a length of 35 feet less than 4 times its width. If the area of the rectangle is 3924 square feet, find the length of the rectangle.

Answer 1

Explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

A rectangle has a length of 35 feet less than 4 times its width. This means that

L = 4W - 35

The area of a rectangle is expressed as L×W = LW

If the area of the rectangle is 3924 square feet, it means that

LW = 3924 - - - - - - -1

Substituting L = 4W - 35 into equation 1, it becomes

W(4W - 35) = 3924

4W^2 - 35W = 3924

4W^2 - 35W - 3924 = 0

4W^2 + 109W - 144W - 3924 = 0

W(4W + 109) -36(4W + 109) = 0

(W - 36)(4W + 109) = 0

W - 36 = 0 or 4W + 109 = 0

W = 36 W = -109/4 = - 27.25

Since the width cannot be negative, the width will be 36 feet

The length will be 3924/36 = 109 feet

Answer 2

width = 36

length = 109

Explanation:

width: x

length: 4x - 35

x * (4x - 35) = 3924

4x^2 - 35x = 3924

4x^2 - 35x - 3924 = 0

(4x + 109)(x - 36) = 0

x = -109/4 or x = 36

Obviously we have to use x = 36 because you can't have a rectangle with negative lengths and widths lol.

width = 36

length = 4(36) - 35 = 144 - 35 = 109