Question

Write a linear equation to represent the given problem and then solve the problem.

The perimeter of a college basketball court is 96 meters and the length is 14 meters more than the width. What are the dimensions?

Perimeter = 2 x Length + 2 x Width

Answer 1

Explanation:

Let L be the length and W the width

Perimeter of a rectangle is P = 2L + 2W

We are told that L = W + 14 (m) [the length is 14 meters more than the width]

Area of a rectangle is A = L*W

We learn that A = 96 m^2

L*W = 96

Since L = W + 14, we can substitute:

L*W = 96

(W + 14)*W = 96 m^2

W^2 + 14W = 96

W^2 + 14W - 96 = 0

The solution to W in the above equation is 5.04 m

This means L = 5.04 m + 14 m

L = 19.04 meters

Perimeter = 2W + 2L

Perimeter = 2(5.04) + 2(19.04) = 96 m^2