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?
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)