A ladder 13m long when set against the wall of a house, just reaches a window at a height of 12m from the ground. How far is the ladder away from the house?

The ladder, the wall, and the ground form a right-angled triangle.
The length of the ladder is the hypotenuse, $c = 13$ m.
The height the ladder reaches on the wall is one leg, $a = 12$ m.
The distance of the ladder's foot from the house is the other leg, $b$, which we need to find.

The Pythagorean theorem states that $a^2 + b^2 = c^2$.
Substitute the given values into the formula:

Subtract 144 from both sides:

Take the square root of both sides:

The ladder is $\boxed{\text{5 m}}$ away from the foot of the house.