SOLUTION: A rectangular swimming pool measures 25m by 6m. It is surrounded by a path of uniform width. If the area of the path is 102m2, find the width of the path.

Question 152202: A rectangular swimming pool measures 25m by 6m. It is surrounded by a path of uniform width. If the area of the path is 102m2, find the width of the path.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rectangular swimming pool measures 25m by 6m. It is surrounded by a path of uniform width. If the area of the path is 102m2, find the width of the path.
.
"area of path" equals "area of pool and path" minus "area of pool"
.
Let x = width of the path
then
"area of pool and path" = (x+25)(x+6) = x^2+31x+150
.
"area of pool" = 25*6 = 150
.
The problem gave us the "area of path" as 102 sq meters
.
Putting it all together we have:
"area of path" equals "area of pool and path" minus "area of pool"
102 = (x^2+31x+150) - 150
102 = x^2+31x+150 - 150
102 = x^2+31x
0 = x^2+31x-102
.
Factoring the right we have:
0 = (x-3)(x+34)
x = {3,-34}
Since a negative number doesn't make sense our solution is therefore:
3 meters is the width of the path

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