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.

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.

Interpret the concepts of the task and translate them into mathematics. (RESTATE THE PROBLEM IN YOUR OWN WORDS)

Answer 1

you want the area of the deck-and-pool to be 832ft^2 greater than just the pool. So, solve for w in

(w+8)(3w+8) - 3w^2 = 832

Having gotten w, you can now determine the size of the pool.

Sounds to me like the problem is poorly stated. You already know the size of the pool. You ought to be trying to figure the area of the deck if you want it to be 4' wide. Unless you can change the size of the pool to accommodate the available concrete . . .