Let's assume
length of rectangle is L
width of rectangle is W
we can find perimeter
perimeter =2L+2W
now, we are given
perimeter =36
so, we get
[tex]2L+2W=36[/tex]
now, we can solve for L
[tex]L+W=18[/tex]
[tex]L=18-W[/tex]
now, we can find area
[tex]A=L\times W[/tex]
we are given area =80
so, we get equation as
[tex]L\times W=80[/tex]
now, we can plug back L
[tex](18-W)\times W=80[/tex]
now, we can solve for W
[tex]18W-W^2=80[/tex]
[tex]W^2-18W+80=0[/tex]
[tex](W-8)(W-10)=0[/tex]
[tex]W=8,W=10[/tex]
now, we can find length
At W=8:
[tex]L=18-8[/tex]
[tex]L=10[/tex]
At W=10:
[tex]L=18-10[/tex]
[tex]L=8[/tex]
So, dimensions of rectangle are
Length of rectangle is 10cm
Width of rectangle is 8cm
OR
Length of rectangle is 8cm
Width of rectangle is 10cm ..............Answer
