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?

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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) About Me  (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

x%5E2%2B26x-672++++=0 , we have quadratic equation to solve

x+=+%28-26+%2B-+sqrt%28+26%5E2-4%2A1%2A%28-672%29+%29%29%2F%282%2A1%29+

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

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