Question 1021231
1.{{{L*W=60}}}
2.{{{(L+2)(W+2)=2*60=120}}}
From 1,
{{{W=60/L}}}
Substituting,
{{{(L+2)(60/L+2)=120}}}
{{{60+2L+120/L+4=120}}}
{{{2L+120/L=56}}}
Multiply by L,
{{{2L^2+120=56L}}}
{{{2L^2-56L+120=0}}}
{{{L^2-28L+60=0}}}
{{{L^2-28L+196+60=196}}}
{{{(L-14)^2=136}}}
{{{L-14=0 +- sqrt(136)}}}
{{{L=14 +- sqrt(136)}}}
{{{L=14 +- 4sqrt(37)}}}
To find W,
{{{W=60/L}}}
{{{W=60/(14+-4sqrt(37))}}}
{{{W=14+- 4 sqrt(37)}}} interchanging +-.
So,
{{{L=14+4sqrt(37)}}},{{{W=14-4sqrt(37)}}}
or
{{{L=14-4sqrt(37)}}},{{{W=14+4sqrt(37)}}}