SOLUTION: A rectangular garden is 60 ft by 80 ft. Part of the garden is torn up to install a sidewalk of uniform width around the garden. The new area of the garden is one sixth of the old a

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Question 628205: A rectangular garden is 60 ft by 80 ft. Part of the garden is torn up to install a sidewalk of uniform width around the garden. The new area of the garden is one sixth of the old area. How wide is the sidewalk?
60-x, 80-x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular garden is 60 ft by 80 ft.
Part of the garden is torn up to install a sidewalk of uniform width around the garden.
The new area of the garden is one sixth of the old area.
How wide is the sidewalk?
:
Let x = the width of the walk
:
The new dimensions of the garden will be (60-2x) by (80-2x)
:
Find the original area: 60*80 = 4800 sq/ft
Find the new area: 1%2F6*4800 = 800 sq/ft
:
(60-2x)*(80-2x) = 800
FOIL
4800 - 120x - 160x + 4x^2 = 800
Combine on the left as a quadratic equation
4x^2 - 280x + 4800 - 800 = 0
4x^2 - 280x + 4000 = 0
simplify divide by 4
x^2 - 70x + 1000 = 0
Factors to
(x-20)(x-50) = 0
Two solutions
x = 50, not reasonable
and
x = 20 ft is the width of the walk
:
:
Check this with the new dimensions (2x = 40):
(80-40)*(60-40) = 800 sq/ft