We can pose the question in the following way:
[tex]l=2w+5[/tex]We have that the perimeter in a rectangle is:
[tex]P=2l+2w[/tex]We can substitute the first equation in the second equation:
[tex]P=2\cdot(2w+5)+2w_{}\Rightarrow P=4w+10+2w\Rightarrow P=6w+10[/tex]Then, we have that P = 34. Thus:
[tex]34=6w+10\Rightarrow6w=34-10\Rightarrow6w=24\Rightarrow w=\frac{24}{4}\Rightarrow w=6[/tex]We can substitute this value of w = 6 in the first equation, then:
[tex]l=2w+5\Rightarrow l=2\cdot(6)+5\Rightarrow l=12+5\Rightarrow l=17_{}[/tex]Then, the length of the rectangle is l = 17 units.
