SOLUTION: A 60-ft. by 80-ft. parking lot is torn up to install a sidewalk of uniform width around its perimeter. The new area of the parking lot is two-thirds of the old area. How wide is th

Algebra ->  Equations -> SOLUTION: A 60-ft. by 80-ft. parking lot is torn up to install a sidewalk of uniform width around its perimeter. The new area of the parking lot is two-thirds of the old area. How wide is th      Log On


   

Question 882284: A 60-ft. by 80-ft. parking lot is torn up to install a sidewalk of uniform width around its perimeter. The new area of the parking lot is two-thirds of the old area. How wide is the sidewalk?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the areas of the new parking lot and the sidewalk is 60*80 square feet.

New lot area is %282%2F3%29%2860%2A80%29.
The parking lot area is also shorter in both dimensions by 2 times the width w of the sidewalk. The factor 2, because each dimension has two ends. Try drawing a picture to help see.

highlight_green%28%2860-2w%29%2880-2w%29=%282%2F3%29%2A%2860%2A80%29%29
4800-160w-120w%2B4w%5E2=4800
4w%5E2-280w%2B4800=4800
4w%5E2-280w=0
w%5E2-70=0
w%5E2=70=7%2A2%2A5
highlight%28w=sqrt%2870%29%29

8 feet 4 inches plus maybe 3/8 inch

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A 60-ft. by 80-ft. parking lot is torn up to install a sidewalk of uniform width around its perimeter. The new area of the parking lot is two-thirds of the old area. How wide is the sidewalk? 


Quadratic equation formed: W%5E2+-+70W+%2B+800+=+0

W, or width of sidewalk:   highlight_green%28highlight_green%2814.3845%29%29      OR	   55.6155 (ignore)

You can do the check!! 



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