Question

A 6.5 m ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall. The height it would reach on the wall is

• A. 3.0 m
• B. 4.0 m
• C. 5.0 m
• D. 6.0 m

Hint:

Recognize the 5-12-13 Pythagorean triple. Here, $2.5, 6.0, 6.5$ is just $0.5 \times (5, 12, 13)$.

Answer 1

The Correct Option is D

Step 1: Concept
This problem can be modeled as a right-angled triangle where the ladder is the hypotenuse ($c$), the distance from the wall is the base ($a$), and the height on the wall is the perpendicular ($b$).

Step 2: Analysis
According to the Pythagoras theorem: $a^2 + b^2 = c^2$. Given $c = 6.5$ m and $a = 2.5$ m.

Step 3: Reasoning
$(2.5)^2 + b^2 = (6.5)^2$
$6.25 + b^2 = 42.25$
$b^2 = 42.25 - 6.25 = 36$
$b = \sqrt{36} = 6$ m.

Step 4: Conclusion
The ladder reaches a height of 6.0 m on the wall. Final Answer: (D)