What are its dimensions?

Question

Someone installs 96 feet of electric fencing around a rectangular headquarters. If the headquarters covers 540 square feet, what are its dimensions? 

Answer 1

The two equations needed to solve this problem are as follows:

 

Let L = the length of the rectangle

Let W = the width of the rectangle

 

Perimeter of a rectangle:

P = L+L+W+W = 2L+2W

 

Area of a rectangle:

A = L*W

 

We are told that the perimeter of the fencing = 96. Therefore:

2L + 2W = 96

L + W = 48

L = 48 - W

 

We are also told that the area of the fencing is 540 sq ft. Therefore,

L*W = 540

 

We now have two equations and two unknowns, so we can solve.

 

Substitute L into the second equation:

 

(48 - W)W = 540

-W² + 48W = 540

W² - 48W = -540

W² - 48W + 540 = 0

 

(W-30)(W-18) = 0

 

Therefore W either equals 30 or 18.

 

We know that L + W = 48.

If L = 30, then W = 18

If W = 30, then L = 18

 

Therefore, the dimensions of the fencing are 30 x 18