Question 359966: I'm confused on how to solve this problem completely. Can you show me how to do it? It's a word problem.
A rectangular swimming pool is 7 ft longer than it is wide. A wooden walk 1 ft wide is placed around the pool. The area covered by the pool and the walk is 58 square feet greater than the area covered by the pool alone. What are the dimensions of the pool?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular swimming pool is 7 ft longer than it is wide.
A wooden walk 1 ft wide is placed around the pool.
The area covered by the pool and the walk is 58 square feet greater than
the area covered by the pool alone.
What are the dimensions of the pool?
:
Let x = the width of the pool
then
(x+7) = the length of the pool
find the area of the pool:
x(x+7) = x^2 + 7x
:
A 1 ft walkway will add 2 ft to each of the pool dimensions, giving the over all dimensions of:
(x+2) = overall width
and
(x+9) = over length
Find the overall area:
FOIL (x+2)*(x+9) = x^2 + 9x + 2x + 18 = x^2 + 11x + 18
:
Overall area - pool area = 58 sq/ft
(x^2 + 11x + 18) -(x^2 + 7x) = 58
Remove brackets
x^2 + 11x + 18 - x^2 - 7x = 58
the x^2's cancel, combine x's on the left, numbers on the right
11x - 7x = 58 - 18
4x = 40
x = 10 ft is the width of the pool
then
10 + 7 = 17 ft is length of the pool
:
:
Check this by finding the difference between the overall area and pool area
overall area: 12 by 19
(12*19) - (10*17) =
228 170 = 58 sq/ft as given, confirms our solutions
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Did the unconfuse you somewhat, any questions?
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