SOLUTION: Glenn cuts half a rectangular lawn, 40m by 30m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangular left. How wide a strip does Glenn cut so that

Question 324589: Glenn cuts half a rectangular lawn, 40m by 30m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangular left. How wide a strip does Glenn cut so that they share the work equally? I need to solve using the quadratic formula. Thank You in advance.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Glenn cuts half a rectangular lawn, 40m by 30m, by mowing strips of equal width around the perimeter.
Brad cuts the small rectangular left.
How wide a strip does Glenn cut so that they share the work equally?
:
Find the area of the whole lawn: 40 * 30 = 1200 sq/m
then half of lawn: 1200/2 = 60 sq/m
:
Let x = width of the strip mown by Glenn equal half the area
:
Dimension of the remaining rectangle
(40-2x) by (30-2x)
:
Half the area:
(40-2x)(30-2x) = 600
FOIL
1200 - 80x - 60x + 4x^2 = 600
:
1200 - 140x + 4x^2 - 600 = 0
Arrange as a quadratic equation
4x^2 - 140x + 600 = 0
Simplify, divide by 4
x^2 - 35x + 150 = 0
Factor
(x-5)(x-30) = 0
The reasonable solution is:
x = 5 m is the width of Glenn's strip
:
:
Check solution by finding the area of the remaining rectangle
40-10)*(30-10) = 600
:
:
Note if they insist on the quadratic formula, solve;

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