Question

If a 30 meter ladder is placed against a wall such that it just reaches the top of the wall, if the horizontal distance between the wall and the base of the ladder is 1/3rd of the length of ladder, then the height of wall is :

• A. 25 meter
• B. 20√2 meter
• C. 20√3 meter
• D. 20 meter

Answer 1

The Correct Option is B

To solve the problem of finding the height of the wall, we will use the Pythagorean Theorem, which is applicable here because the ladder, the wall, and the ground form a right-angled triangle.

1. The length of the ladder is given as 30 meters. This will be the hypotenuse of the right-angled triangle.
2. The horizontal distance between the wall and the base of the ladder is one-third of the length of the ladder. Thus, \(d = \frac{1}{3} \times 30 = 10 \text{ meters}\).
3. Let the height of the wall be \( h \). According to the Pythagorean Theorem:

\(h^2 + d^2 = \text{(ladder length)}^2\) 

Substituting the known values:

\(h^2 + 10^2 = 30^2\)

Simplifying, we get:

• \(h^2 + 100 = 900\)
• \(h^2 = 900 - 100 = 800\)
• \(h = \sqrt{800} = \sqrt{16 \times 50} = 4 \sqrt{50} = 20\sqrt{2}\)

Therefore, the height of the wall is \(20\sqrt{2}\) meters.

Thus, the correct answer is 20√2 meter.