To solve this problem, we can use the Pythagorean theorem. We have a right triangle where:
- The height of the wall (12 feet) represents one leg of the triangle.
- The distance from the base of the house to the base of the ladder (let's call this distance \( x \)) represents the other leg of the triangle.
- The length of the ladder (15 feet) represents the hypotenuse of the triangle.
According to the Pythagorean theorem, we can write the equation:
\[ x^2 + 12^2 = 15^2 \]
Calculating \( 12^2 \) and \( 15^2 \):
\[ x^2 + 144 = 225 \]
Now, we can isolate \( x^2 \):
\[ x^2 = 225 - 144 \]
\[ x^2 = 81 \]
Next, we take the square root of both sides to find \( x \):
\[ x = \sqrt{81} = 9 \]
Thus, the distance from the base of the house where the ladder should be placed is 9 feet.