SOLUTION: A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width on all sides.If the patio area equals the area of the pool, how wi
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Question 254933: A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width on all sides.If the patio area equals the area of the pool, how wide is the distance from the pool edge to the patio edge?
If x represents the width of the patio, then which of the following equations could be used to solve the word problem?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular pool has dimensions of 40 ft. and 60 ft.
The pool has a patio area around it that is the same width on all sides.
If the patio area equals the area of the pool, how wide is the distance from the pool edge to the patio edge?
:
x = the width of the patio
:
Find the area of the pool: 40 * 60 = 2400 sq/ft, therefore:
Pool and the patio = 2(2400) = 4800 sq/ft
:
The equation to find x
(2x+40)*(2x+60) = 4800
FOIL
4x^2 + 120x + 80x + 2400 = 4600
:
4x^2 + 200x + 2400 - 2400 = 0
:
4x^2 + 200x - 2400 = 0
Simplify, divide by 4
x^2 + 50x - 600 = 0
Factor
(x+60)(x-10) = 0
The positive solution is what we want here
x = 10 ft is the width around the pool
:
:
Check solution, find the total area
(60 + 2(10)) * (40 + 2(10)) = 4800
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