Final answer:
To find the new height that the ladder reaches after being pulled 4 feet away from the house, we need to use the Pythagorean theorem twice. In the initial position, we calculate the distance from the base of the house to the ladder and then use the new base distance to calculate the new height. The ladder now reaches approximately 16 feet up the side of the house.
Step-by-step explanation:
The question is asking us to find out how far up the side of the house a 40-foot ladder will reach if it's pulled 4 feet farther from the base of the house, given that it initially reached up 24 feet. This is a geometry problem involving right triangles and the Pythagorean theorem. The original and the new positions of the ladder form two right triangles with the wall of the house and the ground. The ladder itself represents the hypotenuse of these right triangles.
To solve the problem, we first find the original distance from the base of the house to the ladder using the Pythagorean theorem: a2 + b2 = c2, where c is the length of the ladder (40 feet), and b is the height the ladder reaches up the side of the house (24 feet). Thus, a2 + 242 = 402. Solving for a, we find that a = 32 feet.
Now, when Lily pulls the ladder 4 feet farther from the house, the new base distance from the house to the ladder is 32 feet + 4 feet = 36 feet. We apply the Pythagorean theorem again with this new base, a: 362 + b2 = 402. Solving for b gives us the new height the ladder will reach on the side of the house.
Calculating b, we get: b = sqrt(402 - 362), which is about 16 feet. Therefore, after pulling the ladder 4 feet away from the house, it will now reach approximately 16 feet up the side of the house.