For any rectangle the dimensions are given by:
[tex]w:width \\ \\ l:Length[/tex]
So the perimeter (P) is given by the following equation:
[tex]P=2(w+l)[/tex]
And the area is:
[tex]A=w\times l[/tex]
We know that:
[tex]P=20units \\ \\ A=25units^2[/tex]
By substituting:
[tex]20=2(w+l) \\ \\ \therefore w+l=10 \ \ldots eq1 \\ \\ \\ 25=w\times l \ldots eq2[/tex]
Solving for [tex]w[/tex] from eq1:
[tex]w=10-l[/tex]
Substituting into eq2:
[tex]25=(10-l)\times l[/tex]
Then:
[tex]\text{Solving for l:} \\ \\ \\ 10l-l^2=25 \\ \\ 10l-l^2-25=25-25 \\ \\ -l^2+10l-25=0 \\ \\ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ a=-1,\:b=10,\:c=-25 \\ \\ \\ l_{1,\:2}=\frac{-10\pm \sqrt{10^2-4\left(-1\right)\left(-25\right)}}{2\left(-1\right)} \\ \\ l_{1,\:2}=\frac{-10\pm \sqrt{0}}{2\left(-1\right)} \\ \\ l=5[/tex]
Solving for w:
[tex]w=10-5=5[/tex]
So this rectangle is a square and is shown below.
