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?

Answer 1

Answer:

Step-by-step 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