Question 623137: Glenn cuts half a rectangular lawn, 40x30, by mowing strips of equal width around the perimeter. Brad cuts the small rectangle left. How wide a strip does Glenn cut so that they share the work equally,
I calculated the area of the lawn to be 1200m^2 and the perimeter to be 140m but don't know how to proceed from here.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Glenn cuts half a rectangular lawn, 40x30, by mowing strips of equal width around the perimeter.
Brad cuts the small rectangle left.
How wide a strip does Glenn cut so that they share the work equally,
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Then we know half the lawn will have an area of 600 sq/ft
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Let x = the width of the strip to be cut equally around the outside of the lawn.
then the remaining rectangle area:
{40-2x)*(30-2x) = 600
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FOIL and arrange as a quadratic equation
1200 - 80x - 60x + 4x^2 - 600 = 0
4x^2 - 140x + 600 = 0
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Simplify, divide by 4
x^2 - 35x + 150 = 0
;
Factors to
(x - 5)(x - 30) = 0
Two solutions but only one will make sense
x = 5 ft strip all the way around to leave half the lawn remaining
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:
Check this by finding the dimensions and area of the remaining rectangle
A five foot strip will subtract 10 ft from each dimension
(40-10)(30-10) =
30 * 20 = 600 sq/ft
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