SOLUTION: A factory is to be built on a lot measuring 270 ft by 360 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factor
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Question 353399: A factory is to be built on a lot measuring 270 ft by 360 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory.
What must the width of the lawn be?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The area of the rectangle defined by the outside edge of the lawn is 
square feet. Since the lawn area and the factory area have to be equal, each is one half of that value, or 
. Let 
represent the width of the lawn. Since the lawn goes all the way around the factory, the dimensions of the factor have to be 
by 
.
So we can write:
(360\ -\ 2x)\ =\ 48600)
Multiply the binomials using FOIL, collect like terms, and solve the quadratic for . One of the roots will be too large and therefore extraneous. The correct answer is the smaller of the two roots.
John
My calculator said it, I believe it, that settles it
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