SOLUTION: a rectangular lawn is 80 ft by 60ft. part of the lawn is torn up to install a sidewalk of equal width around the lawn. The new area of the lawn is 800 ft^2. how wide is the side

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Question 197653: a rectangular lawn is 80 ft by 60ft. part of the lawn is torn up to install a sidewalk of equal width around the lawn. The new area of the lawn is 800 ft^2. how wide is the sidewalk?
Hi - I can't figure this out. I know the area of the first rectangle is 4800 ft^2. Once I reduce the lawn I think the length is 40 ft and the length is 20 ft. That leaves 4000 ft of area. I don't konw how to find the width of the sidewalk. Thanks for your help.
This is not from a textbook but a worksheet my teacher gave us.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a rectangular lawn is 80 ft by 60ft. part of the lawn is torn up to install a sidewalk of equal width around the lawn. The new area of the lawn is 800 ft^2. how wide is the sidewalk?
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Draw the picture of a rectangle inside a rectangle.
The outer triangle is 80 by 60 = 4800 sq ft.
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Let the width of the sidewalk be "x"
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The inner rectangle has dimensions 80-2x and 60-2x
The area of the inner rectangle is (80-2x)(60-2x) = 4800 -120x -160x + 4x^2
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Equation:
Area of the inner rectangle = 4x^2 - 280x +4800 = 800 sq. ft.
Simplify and solve:
x^2 - 70x + 1000 = 0
(x-20)(x-50) = 0
Realistic answer:
x = 20 ft (width of the sidewalk)
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Cheers,
Stan H.