Let W be width and L be length. So 1st eq is 2W=5/12 L -> W =5/12 L

Length of diagonal = $\sqrt{L^2 + W^2 }$

=$L \sqrt{(1+ 25/144)}$

= $L \sqrt{(169/144)}$

= $\frac{13}{12} L$

Perimeter = $2(L+W)$
= $2 L ( \frac{5}{12} +1)$
= $2 L ( \frac{17}{12})$
= $\frac{34}{ 12} L$

Solving Perimeter : Length of diagonal we get $\frac{34}{13}$

So ans is E