Question 1010622
The four questions are all very much alike, except for the material of the rectangular piece and the values.


Dimensions x and y.
Perimeter p is known.
x and y are related by some known factor, k.
y=kx, and either variable might be taken as width or length, depending on how the described specific problem is arranged.
Question asks for area, the value of xy.


KNOWN: p, k
UNKNOWN: x, y


Each of the four problems goes this way.
{{{system(p=2x+2y,y=kx)}}}


{{{p=2x+2(kx)}}}
{{{(2+2k)x=p}}}
{{{highlight(x=p/(2+2k))}}}


Use x to solve for y.
{{{y=kx}}}
{{{y=k(p/(2+2k))}}}
{{{highlight(y=kp/(2+2k))}}}




Finally, each of the questions asks for area, xy.
{{{highlight_green((kp^2)/(2+2k)^2)}}}
which you might want as
{{{highlight((kp^2)/(4(1+k)^2))}}}