SOLUTION: A pool measuring 10 meters by 16 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 832 square meters, what is the width of the path?

Question 451551: A pool measuring 10 meters by 16 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 832 square meters, what is the width of the path?
Answer by pedjajov(51) (Show Source): You can put this solution on YOUR website!
Path around the pool altogether with pool creates a new rectangle with

- length equal to the length of the pool increased by the width of the path
- width equal to the width of the pool increased by the width of the path

If we mark width of the path with x we get the following formula for the area of the new rectangle

(10+x)(16+x) =832, do the multiplication
160+10x+16x+x^2=832, combine numbers and terms with x
x^2+26x+160 =832, subtract 832 from the both sides

, we have quadratic equation to solve

Two solutions we get are x = 16 or x = -42

Only acceptable solution is a positive number so x = 16 meters.

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