Question 937116
Original rectangle:   w for width, L for length.
Let p=19.9, the perimeter.


New rectangle:  2w for width and still L for length.
Let P=25.7, the perimeter of the newer, newer, BIGGER rectangle.
Notice different case levels for each rectangle perimeter.



EQUATIONS


{{{system(2w+2L=p,2*2w+2L=P)}}}


Simplify the system to
{{{system(2w+2L=p,4w+2L=P)}}}
The unknowns for which to solve are w and L.  P and p are already known, given.


Elimination Method is a good way to begin handling the system.


{{{4w+2L-(2w+2L)=P-p}}}
{{{2w=P-p}}}
{{{highlight(w=(P-p)/2)}}}, the symbolic result for width w.


Taking the simple system but multiplying first equation by 2,
{{{system(4w+4L=2p,4w+2L=P)}}}
Now subtract the second equation from the first equation to eliminate w.
{{{4w+4L-(4w+2L)=2p-P}}}
{{{2L=2p-P}}}
{{{highlight(L=(2p-P)/2)}}}, symbolic result for length L.