SOLUTION: A rectangular lawn is 60 ft by 80 ft. How wide a uniform strip must be cut around the edge in order that 1/6 of the grass be left uncut?

Question 371330: A rectangular lawn is 60 ft by 80 ft. How wide a uniform strip must be cut around the edge in order that 1/6 of the grass be left uncut?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular lawn is 60 ft by 80 ft.
How wide a uniform strip must be cut around the edge in order that 1/6 of the grass be left uncut?
:
Find the area: 60 * 80 = 4800 sq/ft
Find 1/6 of the ares: * 4800 = 800 sq/ft
:
Let x = the width of the uniform strip
then
(60-2x) by (80-2x) will be dimensions of the uncut portion
:
An area equation
(60-2x) * (80-2x) = 800
FOIL
4800 - 120x - 160x + 4x^2 = 800
Arrange 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
and
x = 20 ft is the width of the strip. (this is the only reasonable solution)
:
:
Check by finding the area
(60-40) * (80-40) =
20 * 40 = 800
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