The perimeter of a rectangle is given as:
[tex]P_{rect}=2w+2l[/tex]
We know that
[tex]l=\frac{1}{3}*w{/tex]
as the length is one-third of the width. Now we can plug numbers in:
[tex]72=2w+\frac{2}{3}w = 72=\frac{8}{3}w[/tex]
Now we can solve for width:
[tex]w=27[/tex]
And if the length is one-third the width, we know that
[tex]27*\frac{1}{3} = 9
w=9[/tex]
And [tex]A_{rect}=lw[/tex]
So now we plug in numbers:
[tex]A_{rect}=27*9 = 243[/tex]
