We can write equations, using x and y as the length and width:

xy=40
2x+2y=26

Divide the second equation by two to get:
xy=40
x+y=13

Thus, x=13-y.

We now have (13-x)x=40, so

and 

Factoring, we get:
(x-5)(x-8)=0

So, x can be either 5 or 8 (and y will be the other option).  Thus, the length and width are 8 and 5.