When you draw this out, what you have is a right triangle problem. The height of the rope from the ground is 12 (a side), the distance she is from the base of the tree is 5 (a side), and the length of the rope is the hypotenuse. Use Pythagorean's Theorem to find the length of the hypotenuse: 5^2+12^2 = c^2 or
25+144 = c^2 and c^2 = 169, which makes the length of the rope come out to be 13 feet long.