Let [tex]l[/tex] and [tex]w[/tex] be, respectively, the length and the width of the rectangle.
If the length is 4 inches more than the width, we have
[tex]l = w+4[/tex]
Moreover, the perimeter of a rectangle is given by
[tex]2(l+w)[/tex]
And we can substitute [tex]l=w+4[/tex] to get
[tex]2(w+4+w)=2(2w+4)=4w+8[/tex]
We know that the perimeter is 34 inches:
[tex]4w+8=34 \iff 4w = 26 \iff w = \dfrac{26}{4}=6.5[/tex]
Which implies
[tex]l=w+4=6.5+4=10.5[/tex]
