Answer:
The length is APPROXIMATELY equal to 12.4.
Explanation:
Use the converse of the Pythagorean Theorem (
+
=
[where "c" is both the longest side and the hypotenuse]) since a rectangle's diagonals will always cut it into two right triangles:


169-16=153.
≈ 12
or

or if the problem has to be exact (using radicals)
3*

I hope this helps ;)