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

Question 407949: Glen cuts half a rectangular lawn, 40 m by 30 m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glen cut so that they share the work equally?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Glenn cuts half a rectangular lawn, 40 m by 30 m by mowing strips of equal width around the perimeter.
Brad cuts the smalle rectangle left.
How wide a strip does Glenn cut so that they share the work equally?
:
Find the total area of the lawn:
40 * 30 + 1200 sq/m
then
600 sq/m = half the lawn
:
Let x = the width of the strip cut by Glenn to leave half the lawn for Brad
:
(40-2x)*(30-2x) = 600
FOIL
1200 - 80x - 60x + 4x^2 = 600
Arrange as a quadratic equation
4x^2 - 140x + 1200 - 600 = 0
4x^2 - 140x + 600 = 0
Simplify, divide by 4
x^2 - 35x + 150 = 0
Factors to:
(x-5)(s-30) = 0
Two solutions, but only one will be reasonable
x = 5 meter strip cut around the outside of the lawn leaves half for Brad
;
:
Check that; (subtract 2(5) from each dimension):
1200 - (30 * 20) = 600
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