Final answer:
By applying the Pythagorean theorem to the scenario where a ladder rests against a building, we find that the height up the side of the building where the ladder reaches is 15 feet when the ladder is 25 feet long. Therefore, the correct answer is C. 15 feet.
Step-by-step explanation:
The question presents a scenario where a ladder is leaning against a building. We need to determine how high up the side of the building the top of the ladder reaches if the distance from the bottom of the ladder to the building is 20 feet shorter than the length of the ladder, and this height is 10 feet less than the length of the ladder. To solve this, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Let the length of the ladder be represented by 'L'. Hence, the base of the ladder from the building is L - 20 feet and the height up the side of the building is L - 10 feet.
Setting up the equation according to the Pythagorean theorem gives us:
(L - 20)^2 + (L - 10)^2 = L^2
Expanding and simplifying the equation gives:
L^2 - 40L + 400 + L^2 - 20L + 100 = L^2
Merging like terms and bringing all terms to one side gives:
L^2 - 60L + 500 = 0
Factoring this quadratic equation, we find that L = 25 feet, which means that the ladder is 25 feet long. This means the height up the side of the building where the ladder reaches is 25 - 10 which equals 15 feet.
Therefore, the correct answer is C. 15 feet.