Question 935404

In the middle of a rectangular room, is a rectangular rug, 13 feet by 15 feet. A strip of hardware floor of uniform width is visible around the rug. If the area of the strip is 60 square feet, how wide (in feet) is the strip
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Let uniform width of hardwood floor, be W
Since shorter side of rug is 13 feet, shorter side of entire room = 13 + 2W 
Since longer side of rug is 15 feet, longer side of entire room = 15 + 2W
Since area of entire room, equals area of rug, plus area of hardwood floor, it can be said that:
{13 + 2W)(15 + 2W) = 60 + 15(13)
{{{195 + 56W + 4W^2 = 60 + 195}}}
{{{195 + 56W + 4W^2 = 255}}}
{{{4W^2 + 56W + 195 - 255 = 0}}}
{{{4W^2 + 56W - 60 = 0}}}
{{{4(W^2 + 14W - 15) = 4(0)}}}
{{{W^2 + 14W - 15 = 0}}}
(W - 1)(W + 15) = 0
W, or width of strip = {{{highlight_green(1)}}} foot         OR         W = - 15 (ignore)