Question 134544
Formula for Area of a rectangle?  A = l*w
Formula for perimeter of a rectangle? P = 2l + 2w

Given A = 189, P = 55

{{{189 = l*w}}}
{{{55 = 2l + 2w}}}

{{{189/w = l }}}
{{{55 = 2(189/w) + 2w }}}
{{{55 = 378/w + 2w }}}
{{{55w = 378 + 2w^2}}}
{{{0 = 2w^2 - 55w + 378}}}

Use the quadratic equation
{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{w = (55 +- sqrt( 55^2-4*2*378 ))/(2*2) }}} 
{{{w = (55 +- sqrt( 3025-3024 ))/(2*2) }}} 
w = 54/4, 56/4
w = 13.5 
l = 14