SOLUTION: A rectangular pool measures 8m by 4m. A deck of unifrom width is to be built all the way around the pool such that the total area of the pool and deck will be 96m^2. Set up and sol

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rectangular pool measures 8m by 4m. A deck of unifrom width is to be built all the way around the pool such that the total area of the pool and deck will be 96m^2. Set up and sol      Log On


   

Question 177922: A rectangular pool measures 8m by 4m. A deck of unifrom width is to be built all the way around the pool such that the total area of the pool and deck will be 96m^2. Set up and solve a quadratic equation to determine the width of the deck.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
the key is it is a uniform in width meaning the same all around the pool
:
so lets call this uniform distance x
:
so the length of the total area is 8+2x and the width is 4+2x. L=8+2x,W=4+2x
:
%288%2B2x%29%284%2B2x%29=96
:
32%2B16x%2B8x%2B4x%5E2=96
:
4x%5E2%2B24x-64=0
:
x%5E2%2B6x-16=0
:
%28x%2B8%29%28x-2%29=0
:
so x is either -8 or 2.....since lengths arent negative our answer is
:
x=2 meters
:
W=4+2x=8 meters