Question 570937
length(l) width(w) perimeter(p) area(a)
given:
{{{2l+2w=p}}} = {{{2(l+w)=p}}} = {{{l+w=p/2}}}
{{{lw=a}}}
{{{p=110}}}
{{{a=684}}}
.
so:
{{{l+w=p/2}}}
{{{l+w=110/2}}}
{{{l+w=55}}}
{{{l=55-w}}}
.
{{{lw=a}}}
{{{(55-w)w=684}}}
{{{w^2-55w=-684}}}
{{{w^2-55w+684=0}}} (684=2*2*3*3*19) , (-36*-19=684) , (-36+-19=-55)
{{{(w-36)(w-19)=0}}}
{{{w=36}}} or {{{19}}}
.
{{{l=55-w}}}
{{{l=55-36}}}
{{{l=19}}} or {{{36}}}
.
36 is the length of the longer side