There are two equations here, and you can use substitution to solve. 

Let L equal the length & W equal the width.

The equation for perimeter is L + W + L + W or 2L + 2W so our first equation is 2L + 2W = 35

The problem tell us the second equation also: the length is 1.3 times the width, or L = 1.3W

Substitute 1.3W for L in the first equation so it reads 2(1.3W) + 2W = 35

Multiply the first expression so the new equation is 2.6W + 2W = 35

Add the first two expressions so the new equation is 4.6W = 35

Divide both sides by 4.6 to solve for W: W = 7.6

Now go back to the second equation and insert the value of W: L = 1.3W = 1.3*7.6) = 9.8

You can check your work and use more than one decimal place for more accuracy.