SOLUTION: A factory is to be built on a lot measuring 200 ft by 210 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factor

Question 343801: A factory is to be built on a lot measuring 200 ft by 210 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 this lawn be, and what are the dimensions of the factory?

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 measuring 200 ft by 210 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 this lawn be, and what are the dimensions of the factory?
:
Let x = the width of the lawn
:
Find the total area of the factory and the lawn: 200 * 210 = 42000 sq/ft
:
Factory area has to equal lawn area, therefore
21000 sq/ft = area of the lawn and the factory
:
The dimensions of the factory: (200-2x) by (210-2x)
:
Find x using the area of the factory
(200-2x) * ( 210-2x) = 21000
42000 - 420x - 400x + 4x^2 = 21000
:
Arrange as a quadratic equation:
4x^2 - 820x + 42000 - 21000 = 0
4x^2 - 820x + 21000 = 0
:
Simplify, divide by 4, results:
x^2 - 205x + 5250 = 0
:
Factors to
(x-30)(x-175) = 0
Two solutions,
x = 30 ft is the solution that makes sense for the width of the lawn
;
Find the dimensions of the factory
Length: 210 - 2(30) = 150 ft
Width: 200 - 2(30) = 140 ft
:
:
Confirm this by finding the area of the factory using these dimensions:
150 * 140 = 21000

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