SOLUTION: A rectangular lawn is 60 feet by 80 feet. How wide a uniform strip must be cut around the edge when mowing the grass in order that half of the grass be cut?

Question 109747: A rectangular lawn is 60 feet by 80 feet. How wide a uniform strip must be cut around the edge when mowing the grass in order that half of the grass be cut?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular lawn is 60 feet by 80 feet. How wide a uniform strip must be cut around the edge when mowing the grass in order that half of the grass be cut?
:
Let x = width of the mowed area
then
Un-mowed area = half the total area
(60-2x)* (80-2x) = (60*80)
:
4800 - 280x + 4x^2 = 2400
:
Arrange as a quadratic equation:
4x^2 - 280x + 4800 - 2400 = 0
:
4x^2 - 280x + 2400 = 0
:
Simplify, divide by 4:
x^2 - 70x + 600 = 0
:
Factor this to:
(x - 60)(x - 10) = 0
:
x = +10 ft uniform strip is the only solution that makes sense.
:
:
Check solution
(60-20) * (80-20) = 2400, half the total area
:
Did this make sense to you? Any questions?
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