SOLUTION: A rectangular field measures 80 ft by 60ft. Part of the lawn is torn up to install a walk of uniform width around it. The area of the new field is one-half the area of the old. How

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Question 787826: A rectangular field measures 80 ft by 60ft. Part of the lawn is torn up to install a walk of uniform width around it. The area of the new field is one-half the area of the old. How wide is the walk.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular field measures 80 ft by 60ft.
Part of the lawn is torn up to install a walk of uniform width around it.
The area of the new field is one-half the area of the old.
How wide is the walk.
:
Find the original area: 80 * 60 = 4800 sq/ft, half the area = 2400 sq/ft
:
Let x = width of the walk,
:
We know the original length and width of field will be reduced by 2x
Therefore:
(80-2x)(60-2x) = 2400
4800 - 160x - 120x + 4x^2 = 2400
Arrange as a quadratic equation
4x^2 - 280x + 4800 - 2400 = 0
4x^2 - 280x + 2400 = 0
simplify, divide by 4
x^2 - 70x + 600 = 0
Factors to
(x-10)(x-60) = 0
only one solution will make sense
x = 10 ft is the width of the walkway
:
:
Check
(80-20)(60-20) = 2400 sq