Question 428592: A rectangular garden measures 80 feet by 60 feet. A large path of uniform width is to be added along both shorter sides and one longer side of the garden. The landscape designer doing the work wants to double the garden's area with the addition of his path. How wide should the path be?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular garden measures 80 feet by 60 feet.
A large path of uniform width is to be added along both shorter sides and one longer side of the garden.
The landscape designer doing the work wants to double the garden's area with the addition of his path.
How wide should the path be?
:
The garden area: 80 * 60 = 4800 sq/ft, double = 9600 sq/ft
:
Let x = the width of the proposed path around the three side
:
Draw a rough diagram of this, it is apparent that the overall length = (2x+80)
and the width = (x+60)
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(2x+80)*(x+60) = the overall area, which is to be 9600 sq/ft
FOIL
2x^2 + 120x + 80x + 4800 = 9600
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Combine like terms to form a quadratic equation
2x^2 + 200x + 4800 - 96
;
Simplify, divide by 2
x^2 + 100x - 2400 = 0
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This will factor to
(x+120)(x-20) = 0
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The positive solution is what we want here
x = 20 ft is the width of the path
;
;
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Check this by finding the overall area including the path
(2(20)+80) * (20+60) =
120 * 80 = 9600 sq/ft
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