Question 27

The base of the ladder is 2√14 ft from the wall.

Using the Pythagorean theorem, we can determine the distance from the base of the ladder to the wall. Given that the ladder is 15 ft long and touches the wall at a height of 13 ft, the distance from the base of the ladder to the wall can be calculated as √(15² - 13²), which simplifies to 2√14 ft.

A) 7 ft

This option is incorrect as it does not satisfy the Pythagorean theorem with the given ladder length of 15 ft and the height of 13 ft. Calculating the distance from the wall using the theorem shows that 7 ft is not the right distance.

B) 2√14 ft

This option is correct because it accurately represents the distance from the base of the ladder to the wall when applying the Pythagorean theorem. The calculation yields 2√14 ft, which is approximately 7.48 ft, validating the relationship between the sides of the triangle formed by the ladder, the wall, and the ground.

C) 7.5 ft

While this option is close to the correct answer, it is not exact. The calculated distance of 2√14 ft is approximately 7.48 ft, which is more precise than the rounded figure of 7.5 ft. Therefore, it does not accurately reflect the exact distance as derived from the Pythagorean theorem.

D) 8 ft

This option is incorrect because it exceeds the calculated distance from the wall based on the measurements provided. The Pythagorean theorem confirms that the distance is less than 8 ft, making this option invalid.

Conclusion

The correct answer, 2√14 ft, is derived from applying the Pythagorean theorem accurately to the given dimensions of the ladder and the height at which it touches the wall. All other options either miscalculate or incorrectly interpret the relationship between the ladder's length and its position against the wall. Hence, option B stands out as the only accurate choice.