Answer:
10 meters
Explanation:
You want the width of the path surrounding an 18 meter by 24 meter pool if the total area of pool and path is 1672 square meters.
Area
The total area of the rectangular shape is the product of its length and width:
A = LW
1672 = (24 +2x)(18 +2x)
418 = (12 +x)(9 +x) . . . . . . . . divide by 4
418 = 108 +21x +x² . . . . . . eliminate parentheses
420.25 = 110.25 +21x +x² . . . . . . add 2.5 to complete the square
20.5 = (10.5 +x) . . . . . . . . . . take the positive square root
10 = x . . . . . . . . . . . . . . subtract 10.5
The width of the path is 10 meters.
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Additional comment
The attached graph shows the two solutions of the original equation written so the solutions are the x-intercepts:
(24 +2x)(18 +2x) -1672 = 0
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