Using the pythagorean theorem we can use the formula to find the length of the house.
a^2 + b^2 = c^2
a and b are side lengths while c is the hypotenuse.
Plug in values to get
5^2 + b^2 = 12^2
25 + b^2 = 144
This is your equation
To solve for b we must isolate it, we can subtract 25 on both sides
b^2 = 119
Take the square root of both sides
b = sqr(119)
b = 10.9
The ladder reaches 10.9 feet.