SOLUTION: Please help me solve this problem. A man built a walk of uniform width around a rectangular pool. If the area of the walk is 203 square feet and the dimensions of the pool are 1

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Please help me solve this problem. A man built a walk of uniform width around a rectangular pool. If the area of the walk is 203 square feet and the dimensions of the pool are 1      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 704243: Please help me solve this problem.
A man built a walk of uniform width around a rectangular pool. If the area of the walk is 203 square feet and the dimensions of the pool are 11 feet by 11 feet, how wide is the walk?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = the width of the walk.
Then the two dimensions of the walk and pool are both (11 + 2*w).
The area of the walkway is the total area minus the pool area or
(1) (11 + 2*w)^2 - 11^2 = 203 or
(2) 121 + 44*w + 4*w^2 - 121 = 203 or
(3) 4*w^2 + 44*w - 203 = 0
Use the quadratic equation to get the positive value of the width as
(4) w = 3.5
Check this value in (1)
Is ((11 + 2*3.5)^2 - 11^2 = 203)?
Is ((11 + 7)^2 - 121 = 203)?
Is (18^2 - 121 = 203)?
Is (324 - 121 = 203)?
Is (203 = 203)? Yes
Answer: The width of the walk is 3.5 feet.