SOLUTION: A rectangular swimming pool is 4ft longer than it is wide. It is surrounded by a deck 3ft wide. Find the dimensions of the pool if the area of the deck is 264ft^2.

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Question 112216: A rectangular swimming pool is 4ft longer than it is wide. It is surrounded by a deck 3ft wide. Find the dimensions of the pool if the area of the deck is 264ft^2.
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
THE POOL IS X(X+4)=(X^2+4X) FT^2
ADDING THE DECK DIMENTIONS WE HAVE:
(X+6)(X+10)-264=(X^2+4X) WITH THE DECK THE TOTAL DIMENTIONS ARE (X+6) & (X+10)
X^2+16X+60-264=X^2+4X CANCELLING OUT THE X^2 TERMS WE HAVE:
16X-4X=204
12X=204
X=204/12
X=17 FT. IS THE WIDTH OF THE POOL.
THUS THE LENGTH IS 17+4=21 FT.
AREA OF THE POOL:
17*21=357 FT^2.
AREA OF THE POOL PLUS THE DECK:
(17+6)(21+6)=23*27=621 FT^2
THE DIFFERENCE IN AREA IS:
621-357=264 FT^2 WHICH IS THE AREA OF THE DECK.