Question 863919
Let x be length and y be width.
Let p be perimeter.
Formula for perimeter is {{{2(x+y)=p}}}.
Your description can be generalized into, "perimeter of a rectangle is p cm. The length,x, of the rectangle is n cm more than m times the width of y."


The description like that symbolically is ... {{{x=n+my}}}.
KNOWN: p, m, n.
UNKNOWN: x, y.


EQUATIONS FOR  A SYSTEM:
{{{2(x+y)=p}}} and {{{x=n+my}}}.
Substitute for x.
{{{2(n+my+y)=p}}}
{{{2n+2my+2y=p}}}
{{{2my+2y=p-2n}}}
{{{y(2m+2)=p-2n}}}
{{{highlight(y=(p-2n)/(2m+2))}}}.  This is one of the dimensions answered.
-
Use the description translated about x to find the symbolic form for x.
{{{x=n+my}}}---From the translation.
{{{highlight(x=n+m((p-2n)/(2m+2)))}}}.   The other dimension answered.
You can stop right there, or you can continue putting into a fully rational form...
{{{x=n(2m+2)/(2m+2)+m(p-2n)/(2m+2)}}}
{{{x=(2mn+2n+mp-2np)/(2m+2)}}}.   This form for the other dimension if you want it this way.


Recall the values given for p, m, and n.