SOLUTION: The length of a rectangular swimming pool is twice its width. The pool is surrounded by a walk that is 2 feet wide. The area of the region consisting of the pool and the walk is 10

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Question 1029553: The length of a rectangular swimming pool is twice its width. The pool is surrounded by a walk that is 2 feet wide. The area of the region consisting of the pool and the walk is 1056 square feet.
(a) Use the method of completing the square to determine the dimensions of the swimming pool.
The length of the pool is ____ feet, and the width of the pool is ____feet.
(b) If the material for the walk costs $8 per square foot, how much would the material cost for the entire walk?
The material would cost $____ .
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Length is L and width is w.
L=2w
-
Let x be the uniform width of the surrounding walkway of the pool.
Let A be the total area of walkway and pool (in only the top surface, of course).
A=1056
x=2
-

The first basic equation directly from the description and assigned variables is %28L%2B2x%29%28w%2B2x%29=A.

Substitute for L.
%282w%2B2x%29%28w%2B2x%29=A
2%28w%2Bx%29%28w%2B2x%29-A=0
2%28w%5E2%2Bwx%2B2wx%2B2x%5E2%29-A=0
highlight_green%282%28w%5E2%2B3wx%2B2x%5E2%29-A=0%29

You can continue this in its purely symbolic form, for the UNKNOWN variable, w. Remember, x and A are KNOWN already. The term to use INSIDE the parentheses to complete the square is %283x%2F2%29%5E2. Watch the groupings very carefully; and go through Complete-the-Square process to solve for w. Substitute the values for x and A whenever you feel you want in the process.

You continue this on your own.