Members of the and#64257;re department lean a 26-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?a)12b)15c)20d)22e)24Correct answer is option 'E'. Can you explain this answer?

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Members of the ﬁre department lean a 26-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?

a)
12
b)
15
c)
20
d)
22
e)
24

Correct answer is option 'E'. Can you explain this answer?

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Members of the ﬁre department lean a 26-foot ladder against a b...

The correct answer is E. To ﬁnd out how far a 26-foot ladder reaches up a building when the base of the ladder is 10 feet away from the building, it is useful to draw a picture, as shown below:

As you can see, the ladder forms the hypotenuse of a right triangle with a length of 26, and the base of the ladder is 10 feet away from the building. Using the Pythagorean Theorem, 26² = 10² + d², where d is the distance up the building. Simplifying you get 676 = 100 + d² → 576 = d² → 24 = d.

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Members of the ﬁre department lean a 26-foot ladder against a b...

Solution:

Given:
- Length of the ladder = 26 feet
- Distance of the base of the ladder from the building = 10 feet

Using the Pythagorean theorem:
- Let the height reached by the ladder on the building be 'h'
- According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.
- Therefore, we have: \( 10^2 + h^2 = 26^2 \)
- \( 100 + h^2 = 676 \)
- \( h^2 = 676 - 100 \)
- \( h^2 = 576 \)
- \( h = \sqrt{576} \)
- \( h = 24 \) feet

Therefore, the ladder reaches 24 feet up the building.
So, the correct answer is option 'E' (24).

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Members of the ﬁre department lean a 26-foot ladder against a b...

The correct answer is E. To ﬁnd out how far a 26-foot ladder reaches up a building when the base of the ladder is 10 feet away from the building, it is useful to draw a picture, as shown below:

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Members of the ﬁre department lean a 26-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?a)12b)15c)20d)22e)24Correct answer is option 'E'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Members of the ﬁre department lean a 26-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?a)12b)15c)20d)22e)24Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Members of the ﬁre department lean a 26-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?a)12b)15c)20d)22e)24Correct answer is option 'E'. Can you explain this answer?.

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