You are building a concrete deck around a rectangular swimming pool. The pool is three times as long as it is wide. The deck will have a constant width of four feet. In order to have enough concrete, you have calculated the area of the deck to be 832 square feet. What are the dimensions of the pool?

I know this has something to do with factoring equations, but I am just so confused on how to set it up.

Question

You are building a concrete deck around a rectangular swimming pool. The pool is three times as long as it is wide. The deck will have a constant width of four feet. In order to have enough concrete, you have calculated the area of the deck to be 832 square feet. What are the dimensions of the pool?

I know this has something to do with factoring equations, but I am just so confused on how to set it up.

anonymous · Answer

If the width of the pool is w, then the length is 3w. 

So, the difference in area between the whole thing and just the pool is the area of the deck: 832 

(w+8)(3w+8) - w(3w) = 832 
w = 24 

So, the pool is 24x72 feet 

Check: 
The pool + deck has area (24+8)(72+8) = 2560 
The pool has area 24*72 = 1728 

2560-1728 = 832