Question 964092
x=width of path
{{{(31yds+2x)(27yds+2x)=2205yds^2}}}
{{{4x^2+116x+837=2205yds^2}}}
{{{4x^2+116x-1368=0}}}
{{{x^2+29x-342=0}}}
{{{(x-9)(x+38)=0}}}
{{{x-9=0}}} {{{or}}} {{{x+38=0}}}
{{{x=9}}} {{{or}}} {{{x=-38}}}
ANSWER: The width of the path is 9 yards.
CHECK:
{{{(31yds+2(9yds))(27yds+2(9yds))=2205yds^2}}}
{{{(49yds)(45yds)=2205yds}}}
{{{2205yds^2=2205yds^2}}}