Final answer:
The question involves finding the length of a ladder based on given distances, forming a right-angled triangle. By employing the Pythagorean theorem and solving an equation, we can determine both the height the ladder reaches on the building and its length.
Step-by-step explanation:
The student is asking about the length of a ladder that is 1 foot longer than the height it reaches on a building, given that the base of the ladder is 7 feet from the building. This is a classic application of the Pythagorean theorem, since we have a right-angled triangle formed by the ladder, the ground, and the height the ladder reaches on the building.
Let's denote the height the ladder reaches on the wall as h feet. According to the problem, the ladder's length is h + 1 feet. Since the ladder forms a right-angled triangle with the ground and the building, we can use the Pythagorean theorem to write the following equation:
h2 + 72 = (h + 1)2
Solving this equation will give us the height that the ladder reaches, and adding 1 to it will give us the length of the ladder.