Question 1050400
{{{x}}} length of the rectangle, in cm
{{{y}}} = width of the rectangle, in cm
{{{xy=18}}}
{{{18=2^red(1)*3^green(2)}}} , so {{{18}}} has {{{(red(1)+1)*(green(2)+1)=2*3=6}}} factors.
Those factors form {{{6/2=3}}} pairs of factors whose product is {{{18}}} .
The pairs/products are:
{{{1*18=18}}} ,
{{{2*9=18}}} , and
{{{3*6=18}}} .
The perimeter of the rectangle is
{{{2(x+y)}}} .
If {{{system(x=18,y=1)}}} , {{{perimeter=2*(1+18)=2*19=38}}} .
If {{{system(x=9,y=2)}}} , {{{perimeter=2*(2+9)=2*11=22}}} .
If {{{system(x=6,y=3)}}} , {{{perimeter=2*(3+6)=2*9=highlight(18)}}} .