Question 943701

A man built a walk of uniform width around a rectangular pool. If the area of the walk is 189 square feet and the dimensions of the pool are 6 feet by 6 feet, how wide is the walk?
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Pool’s area: 6(6), or 36 sq ft
Walk’s area: 189 sq ft
Let walk’s width be W
Dimensions of entire structure: (6 + 2W), and (6 + 2W)
Area of entire structure: {{{(6 + 2W)^2}}}, or {{{36 + 24W + 4W^2}}}
Pool’s area, plus walk’s area, equals area of entire structure, OR
{{{36 + 189 = 36 + 24W + 4W^2}}}
{{{225 = 36 + 24W + 4W^2}}}
{{{4W^2 + 24W + 36 - 225 = 0}}}
{{{4W^2 + 24W - 189 = 0}}}
{{{4W^2 + 42W - 18W - 189 = 0}}}
2W(2W + 21) – 9(2W + 21) = 0
(2W – 9)(2W + 21) = 0
2W = 9					     OR	   	          2W + 21 = 0 
W, or width = {{{9/2}}}, or {{{highlight_green(4.5)}}} ft		     OR	                  2W = - 21 (ignore)