Let l and w be the length and width of the rectangle. We know that [tex]l=2w-4[/tex]
The formula for the perimeter is [tex]P=2(w+l)[/tex]
Using our substitution, it becomes
[tex]P=2(w+2w-4)=2(3w-4)=6w-8[/tex]
We know that the perimeter is 34, so we have
[tex]6w-8=34 \iff 6w=42 \iff w=7[/tex]
The length is 4 less than twice the width, so we have
[tex]l=2\cdot 7 - 4 = 10[/tex]
