SOLUTION: a rectangular lawn is 10 feet long and 9 feet wide. A concrete path of uniform width and covering an area of 120 sq feet is to be constructed to form a border around the lawn. Writ

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Question 865450: a rectangular lawn is 10 feet long and 9 feet wide. A concrete path of uniform width and covering an area of 120 sq feet is to be constructed to form a border around the lawn. Write a suitable equation and solve it to find the width of the concrete path.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Lawn PLUS the path around it, %289%2B2w%29%2810%2B2w%29, using w for the width of the path.

Total Area - Lawn Area = Path Area
highlight_green%28%282w%2B9%29%282w%2B10%29-9%2A10=120%29.
4w%5E2%2B18w%2B20w%2B90-90-120=0
4w%5E2%2B38w-120=0
2w%5E2%2B19w-60=0
-
Discr=19%5E2-4%2A2%28-60%29=19%5E2%2B8%2A60=19%5E2%2B480=841=29%5E2
-
w=%28-19%2Bsqrt%28Discr%29%29%2F4=%28-19%2Bsqrt%2829%5E2%29%29%2F4=%28-19%2B29%29%2F4
w=10%2F4=5%2F2
highlight%28w=2%261%2F2%29 feet.