Question

The surface of a pool table has a perimeter of 26 feet and an area of 36 square feet. What are the dimensions of the pool table?

feet by
feet

Answer 1

Explanation:

pool tables are rectanglar

Perimeter = 2L + 2W = 2(L+W) ---->>> Perimeter/2 = L + W =

Perimeter/2 - W = L

Area = L×W

Two equations and two unknowns and L is substituted into the area equation

---->> Area = (Perimeter/2 - W) x W

Area = (Perimeter x W)/2 - W² solve for W

Area = 36 and Perimeter = 26

36 ft² = (26)( W)/2 ft - W² ft²

36 ft² = 13W ft - W² ft²

W² - 13W + 36 = 0 quadratic equation factor solve for W

(W - 4)(W - 9) = 0

There are two roots

W - 4 = 0 and W - 9 = 0

W = 4 and 9 W = 9 it doesn't make sense needs to be < L

Perimeter/2 - W = L

L = 26/2 - W

= 13 - 4

L = 9 ft and W = 4 ft