Question 43205
width = w
length = 3w + 2
{{{lw = area}}}
{{{(3w + 2)w = 83}}}
{{{3w^2 + 2w - 83 = 0}}}
{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{w = (-2 +- sqrt( 2^2-4*3*(-83) ))/(2*3) }}} 
{{{w = (-2 +- sqrt( 1000 ))/(6) }}}
{{{w = -1/3 + sqrt(2*5*2*5*2*5)/6}}}
{{{w = -1/3 + 10sqrt(10)/6}}} about 4.9371
PLUG:
length = 3w + 2 = length = 3(-1/3 + 10sqrt(10)/6) + 2 = 1 + 5sqrt(10)