Question 122691
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? 
:
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).
:
Let x = the width of the lawn:
:
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)
:
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
:
Divide equation by 4 to simplify
x^2 + 70x + 600 = 0
:
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
:
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