Answer:
The length and width of the rectangle are 12 and 3
Step-by-step explanation:
Perimeter:
[tex]p=2l+2w[/tex]
Area:
[tex]a=lw[/tex]
Write 2 equations and solve:
[tex]36=lw[/tex]
[tex]30=2l+2w[/tex]
Isolate one of the variables in one of the equations:
[tex]36=lw[/tex]
[tex]l=\frac{36}{w}[/tex]
Substitute this in for l in the other equation:
[tex]\frac{72}{w} +2w=30[/tex]
Solve for w (ask in comments if you want me to explain this step):
[tex]w=12,3[/tex]
Plug in one of the solutions into the other equation:
[tex]36=12l[/tex]
[tex]l=3[/tex]
