What are the possible dimensions used to construct the area?

Question

A security fence encloses a rectangular area on one side of a park in a city. Three sides of fencing are used, since the fourth side of the area is formed by a building. The enclosed area measures 648 square feet. Exactly 72 feet of fencing is used to fence in three sides of this rectangle. What are the possible dimensions that could have been used to construct this area?

Answer 1

L + 2W = 72

L = 72 - 2W

 

648 = L · W

648 = (72 - 2W)W

648 = 72W - 2W²

0 = -2W² + 72W - 648

0 = W² - 36W + 324

0 = (W - 18)²

 

The width is 18 feet and the length is 36 feet.