SOLUTION: A man built a walk of uniform width around a rectangular pool. If the area of the walk is 117 sqaure feet and the dimensions of the pool are 16 feet by 20 feet, how wide is the wal

Question 516250: A man built a walk of uniform width around a rectangular pool. If the area of the walk is 117 sqaure feet and the dimensions of the pool are 16 feet by 20 feet, how wide is the walk?
Answer by gc2000(22) (Show Source): You can put this solution on YOUR website!
walk area = area of large rectangle minus area of small rectangle (the small rectangle is the pool).
117 = large rectangle - 320
{add 320 to both sides}
437 = large rectangle area.

{note: walk is equal width.}

walk dimensions: the difference in dimension between large and small rectangle:
small rectangle = 16 * 20
let x be the difference (that is, the walk width)
large rectangle = (16 + x)(20 + x)

substitute:
437 = (16 + x)(20 + x)
437 = 320 + 36x + x^2
{subtract 437 from both sides, then
arrange for factoring}
x^2 + 36x - 117 = 0
{factor}
[first factor 117 to 3 * 3 * 13]
[look to arrange factors so there will be two, one negative, one positive (in view of the negative 117); and whose difference is 36]
[one possibility fits:]
(x + (3*13))(x - 3)
that is
(x + 39)(x - 3)
x = 3, -39
only one is viable:
x = 3

the walk width is 3 ft.

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