Quadratic word problems

Question

The area of a rectangle is 54 ft ² , and the length of the rectangle is 3 ft more than twice the width . Find the dimensions of the rectangle

Answer 1

Hi Teethabrattt, the equation to solve is: A = L * W. Given L = 2W + 3, and A = 54 sq ft.

Substitute for L and solve:

A = (2W + 3) * W

54 = 2W² + 3W

Rewrite:

2W² + 3W - 54 = 0

Factor:

(2W - 9) * (W + 6) = 0

Use the zero property rule:

2W - 9 = 0

W = 9 / 2, or 4.5

W + 6 = 0

W = -6, we can discard this answer because it is negative.

Find L:

L = 2W + 3

L = 2 * 4.5 + 3, or 12

Answer:

The width of the rectangle is 4.5 feet.

The length of the rectangle is 12 feet.

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