SOLUTION: . A square hall has a rug and an uncarpeted area of tile floor bordering it that is 2 feet on each side. What is the size of the carpet if the uncarpeted area is 152 square feet?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: . A square hall has a rug and an uncarpeted area of tile floor bordering it that is 2 feet on each side. What is the size of the carpet if the uncarpeted area is 152 square feet?      Log On

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Question 899001: . A square hall has a rug and an uncarpeted area of tile floor bordering it that is 2 feet on each side. What is the size of the carpet if the uncarpeted area is 152 square feet?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the edge length of the square carpet.
The Entire floor is %28x%2B2%2A2%29%28x%2B2%2A2%29 square feet in area.
The carpet is x%5E2 square feet in area.
Their difference is the uncarpeted 152 sq. ft. area, or
%28x%2B4%29%28x%2B4%29-x%5E2=152
x%5E2%2B8x%2B16-x%5E2=152
8x%2B16=152
8x=152-16
8x=136
highlight%28x=17%29