Question

A pool measuring 18 meters by 24 meters is surrounded by a path of uniform width, as

shown in the figure. If the area of the pool and the path combined is 1672 square meters,
what is the width of the path?

Answer 1

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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