#### Answer

System: $\left\{\begin{array}{l}
l=5+2w\\
2l+2w=34
\end{array}\right.$
Width: $w=4$ cm
Length: $l=13$ cm

#### Work Step by Step

$l$ is 5 more than 2$\times$w $\qquad \Rightarrow\qquad l=5+2w$
Perimeter = 34 $\qquad \Rightarrow\qquad 2l+2w=34$
Substitute $5+2w$ for $l$ in the second equation and solve for $w$
$ 2(5+2w)+2w=34 \quad$ ... distribute, simplify
$ 10+4w+2w=34 \quad$ ... add $-10$
$ 6w=24\quad$ ... divide with $3$
$w=4$ cm
Substitute $4$ for $w$ in $\qquad l=5+2w$
$l=5+2\cdot 4=13$ cm
Width: $w=4$ cm
Length: $l=13$ cm
System: $\left\{\begin{array}{l}
l=5+2w\\
2l+2w=34
\end{array}\right.$
Width: $w=4$ cm
Length: $l=13$ cm
Check:
The area is 13(4)=52.