SOLUTION: A farmer has a 25 ft by 50 ft rectangular field that he wants to reduce to 12% of its original size. How wide of a strip should he cut around the edge of his field to do this?

Question 837050: A farmer has a 25 ft by 50 ft rectangular field that he wants to reduce to 12% of its original size. How wide of a strip should he cut around the edge of his field to do this?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A farmer has a 25 ft by 50 ft rectangular field that he wants to reduce to 12% of its original size.
How wide of a strip should he cut around the edge of his field to do this?
:
Find the original area of the field: 25 * 50 = 1250 sq/ft
:
Let x = the width of the strip cut around the field to reduce size to 12% original
A strip all the way around will reduce the dimensions by 2x
therefore
(25-2x)(50-2x) = .12(1250)
FOIL
1250 - 50x - 100x + 4x^2 = 150
Combine as a quadratic equation
4x^2 - 150x + 1250 - 150 = 0
4x^2 - 150x + 1100 = 0
Factors to
(2x-20)(2x-55) = 0
Two solutions
2x = 55
x = 27.5
and
2x = 20
x = 10 ft strip, the only reasonable solution
:
:
Check this; find the area when dimensions are reduced by 20 ft
(25-20)*(50-20)_ = 150 sq/ft, which is 12% the original
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