Final answer:
The ladder will reach a height of approximately 21.6 feet up the side of the house when it's pulled 3 feet farther from the house.
Step-by-step explanation:
To find the new height up the side of the house that the ladder will reach after being pulled 3 feet farther from the house, we can use similar triangles. The ratio of the new distance from the base to the height reached by the ladder is the same as the ratio of the original distance from the base to the original height reached by the ladder.
Let's call the new distance x and the new height y. We can set up the following equation:
x/24 = (x+3)/40.
Cross-multiplying and solving for x, we find x = 36.
Therefore, the ladder will reach a height of approximately 21.6 feet up the side of the house when it's pulled 3 feet farther from the house.