Question 964995
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W=width; L=length=6W+3ft; A=area=165ft^2
{{{LW=A}}} Substitute for L
{{{(6W+3ft)(W)=165ft^2}}}
{{{6W^2+3Wft=165ft^2}}} Subtract 165ft^2 from each side.
{{{6W^2+3Wft-165ft^2=0}}} Divide by 3
{{{2W^2+W-55=0}}}
{{{(2W+11)(W-5)=0}}}
{{{2W+11=0}}} {{{or}}} {{{W-5=0}}}
{{{2W=-11}}} {{{or}}} {{{W=5}}}
{{{W=-5.5}}} {{{or}}} {{{W=5}}}
ANSWER: The width is 5 feet.
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CHECK:
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{{{L=6W+3ft}}}={{{6(5ft)+3ft=39ft+3ft}}}={{{33ft}}} Length is 33 feet.
{{{LW=A}}}
{{{(33ft)(5ft)=165ft^2}}}
{{{165ft^2=165ft^2}}}