Question 1204421



Let {{{x }}}be the width of the uniform strip floor around the rug.


Then the width of the rug is {{{(27 - 2x) }}}and the length of the rug is {{{(35 - 2x)}}}.


{{{(27 - 2x)(35 - 2x) = 609}}}

{{{4x^2 - 124x + 945 =609}}}

{{{4x^2 - 124x + 945 -609=0}}}

{{{4x^2 - 124x + 336=0}}}

{{{4(x^2 -31x + 84)=0}}}

{{{4 (x - 28) (x - 3) = 0}}}

solutions:

{{{x = 3 }}}
or 
{{{x = 28}}} (rejected as {{{x}}} must be less that the width of the room)

Hence,

 the width of the rug is{{{ 27 - 2(3) = 21ft}}} 
and 
the length of the rug is {{{35 - 2(3) = 29ft}}}