SOLUTION: A rectangular lawn measures 60ft. by 80ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new lawn is {{{2400ft^2}}}. How wide is the

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Question 836017: A rectangular lawn measures 60ft. by 80ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new lawn is 2400ft%5E2. How wide is the sidewalk?
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
New area of the lawn becomes %2860-2w%29%2880-2w%29=2400, using w as the width of the sidewalk.

4%2830-w%29%2840-w%29=4%2A600
%2830-w%29%2840-w%29=600
1200-70w%2Bw%5E2=600
600-70w%2Bw%5E2=0

Try to factor the quadratic expression.
600=100*2*3=2*5*2*5*2*3=2*2*2*3*5*5,,,, if seems too much trouble, just use general solution for a quadratic formula.

Discrim, 70^2-4*600=4900-2400=2500
w=%2870%2B-+sqrt%282500%29%29%2F%282%29
w=%2870%2B-+5%2A10%29%2F2, we must use the positive value.
highlight%28w=10%29 or cross%28w=60%29, only one of them making sense.

Worth a check:
(60-2*10)(80-2*10)=2400?
%2860-20%29%2880-20%29
40%2A60=2400 yes.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular lawn measures 60ft. by 80ft.
Part of the lawn is torn up to install a sidewalk of uniform width around it.
The area of the new lawn is 2400 sq/ft. How wide is the sidewalk?
:
Find the original area: 60 * 80 = 4800 sq/ft
Find the area of the walkway: 4800 - 2400 = 2400
:
let x = the width of the walk
;
(60-2x)*(80-2x) = 2400
FOIL
4800 - 120x - 160x + 4s^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
x = 10 ft, the only one that makes sense