Answer: x = 3
Explanation
A rectangle has all 4 angles of 90 degrees each.
Triangle LMO is a right triangle.
Use the Pythagorean theorem to tie together the 3 sides.
a^2 + b^2 = c^2
(5x)^2 + (36)^2 = (13x)^2
25x^2 + 1296 = 169x^2
1296 = 169x^2 - 25x^2
1296 = 144x^2
x^2 = 1296/144
x^2 = 9
x = sqrt(9)
x = 3
