Posted by **Carolyn** on Tuesday, May 22, 2012 at 7:16pm.

Minnie and Steve have arectangular swimming pool that is 12 ft. wide and 20 feet long. They are going to build a tile border of uniform width around the pool. They have 160 sq. ft. of tile. How wide should the border be?

- algebra 2 -
**Reiny**, Tuesday, May 22, 2012 at 9:00pm
area of pool only = 12x20 = 240 ft^2

let the width of the border be x ft

so area of pool + border

= (12+2x)(20+2x) = 4x^2 + 64x + 240

New area - pool area = tile area

4x^2 + 64x + 240 - 240 = 160

4x^2 + 64x - 160 = 0

x^2 + 16x - 40 = 0

complete the square

x^2 + 16x + 64 = 40 + 64

(x+8)^2 = 104

x+8 = √104

x = ±√104 - 8

x = appr 2.2 ft or a negative, which would be silly

the border should be 2.2 ft wide

(good luck finding a 2.2 ft tile, looks like a lot of wasteful cutting)

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