Question

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches 6 m above the ground. Then the length of the ladder is:

• A. 3.5 m
• B. 4.5 m
• C. 8.5 m
• D. 6.5 m

Hint:

When solving problems involving ladders leaning against walls, visualize the situation as a right triangle and apply the Pythagorean theorem. Ensure all measurements are correctly substituted into the formula to avoid errors.

Answer 1

The Correct Option is D

Step 1: Visualize the Problem.
The ladder forms a right triangle with the wall and the ground. The distance from the foot of the ladder to the wall is \( 2.5 \, \text{m} \), and the height reached by the ladder is \( 6 \, \text{m} \). The length of the ladder is the hypotenuse. Step 2: Apply the Pythagorean Theorem.
\[ \text{Length}^2 = (2.5)^2 + 6^2 = 6.25 + 36 = 42.25. \] Taking the square root: \[ \text{Length} = \sqrt{42.25} = 6.5 \, \text{m}. \] Step 3: Analyze the Options.
Option (1): \( 3.5 \, \text{m} \) — Incorrect.
Option (2): \( 4.5 \, \text{m} \) — Incorrect.
Option (3): \( 8.5 \, \text{m} \) — Incorrect.
Option (4): \( 6.5 \, \text{m} \) — Correct. Step 4: Final Answer.
\[ \boxed{6.5 \, \text{m}} \]