The walk is 4 feet wide
The width of the rectangular pool = 8 feet
The length of the rectangular pool = 12 feet
Let the width of the walkway be w
The combined length of the pool and walkway = 12 + 2w
The combined width of the pool and walk way = 8 + 2w
The total area of the walk and the pool = 320 square feet
Area = Length x Width
320 = (12 + 2w) ( 8 + 2w)
320 = 96 + 24w + 16w + 4w²
4w² + 40w + 96 - 320 = 0
4w² + 40w - 224 = 0
w² + 10w - 56 = 0
w² - 4w + 14w - 56 = 0
w(w - 4) + 14(w - 4) = 0
(w - 4)(w + 14) = 0
w - 4 = 0
w = 4
w + 14 = 0
w = -14
The width of the walk = 4 feet
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