SOLUTION: a pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. if the area of the pool and the path combined 1152 square meters, what is the width of the path

Question 1012561: a pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. if the area of the pool and the path combined 1152 square meters, what is the width of the path
Found 3 solutions by Alan3354, algebra hello, fractalier:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
a pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. if the area of the pool and the path combined 1152 square meters, what is the width of the path
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The difference is 4 meters
Find a pair of factors of 1152 that differ by 4.
Then subtract 18 from the smaller factor, and divide the result by 2.
Answer by algebra hello(55)   (Show Source): You can put this solution on YOUR website!
area of path= 1152-18*22
(18 2x)(22 2x)=1152-396
4(9 x)(11 x)=756
x^2 20x 99-189=0
x^2 20x-90=0
on solving this the value of x gives the width of path
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
Call the width of the path, x.
Then the dimensions of the pool and path will be
(18+x) by (22+x)
We can multiply them, set it equal to 1152 and solve for x...we get
(x+18)(x+22) = 1152
x^2 + 40x + 396 = 1152
x^2 + 40x - 756 = 0
(x + 54)(x - 14) = 0
x = -54 or x = 14
Must be 14 meters.
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