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Question 122691: Please help me solve this word problem!!!!
A factory is to be built on a lot that measures 80m by 60m. A lawn of uniform width, equal to the area of the factory, must surround it. How wide is the strip of lawn, and what are the dimensions of the factory?
The answers should be 10m, 60m by 40m.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A factory is to be built on a lot that measures 80m by 60m. A lawn of uniform width, equal to the area of the factory, must surround it. How wide is the strip of lawn, and what are the dimensions of the factory?
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Find the area of the lot
80 * 60 = 4800
Then
4800/2 = 2400 is the area of the factory (also the area of the lawn).
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Let x = the width of the lawn:
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Make a rough drawing of this, a rectangle (factory) inside a a larger rectangle.
Label the width of strip around the factor as x. Label the lot 80 by 60
It will be apparent that factory will be (80-2x) by (60-2x)
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Therefore we have an area equation of:
(80-2x)*(60-2x) = 2400
FOIL
4800 - 160x - 120x + 4x^2 = 2400
:
4x^2 - 280x + 4800 - 2400 = 0; arrange as a quadratic equation
:
4x^2 + 280x + 2400
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Divide equation by 4 to simplify
x^2 + 70x + 600 = 0
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Factors to:
(x-10)(x-60) = 0
x = +60, not a reasonable answer
and
x = 10 m is the width of the lawn around the factory
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The dimension of the factory then
80 - 20 = 60m
60 - 20 = 40m
:
Check solution finding the areas
Lot area80*60 = 4800
Factory 60*40 = 2400
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minus is lawn = 2400
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