You want to build a rectangular fence which is 8 feet longer than it is wide. the area enclosed by the fence to be 55 square feet. How wide is the fence

Question

it's asking for the smaller side length of the rectangular fence

Answer 1

Hi Ashley,

 

There are three variables here: area, width, and length. You are given length and area, therefore you can solve for width since it is the only unknown.

Area = Width x Length

A = W * L

(55 ft²) = W * (W + 8)

55 ft² = W² + 8W

0 = W² + 8W - 55

From here you can use the quadratic formula to solve.

W = ( -8 (+/-) √( (8)² - 4(-55) ) ) / 2

= -4 (+/-) ( √( 64 + 220 ) / 2 )

= -4 (+/-) 16.85 / 2

= -4 (+/-) 8.425

= 4.425, -12.4

Thus the width is approximately 4.425 ft and the length is 8 more than that, 12.425 feet.

Multiply these numbers together to check your work and you get approximately 55 square feet (~54.98).