A ladder is resting with one end is contact with the top of a wall of height 60 m and the other end on the ground is at a distance of 11 m form the wall. The length of the ladder is :

Options

A. 61 m
B. 71 m
C. 87 m
D. none of these

Answer

To find the length of the ladder resting against the wall, we can use the Pythagorean theorem. The situation describes a right triangle where:

- The height of the wall (one leg of the triangle) is 60 meters.
- The distance from the wall to the base of the ladder (the other leg of the triangle) is 11 meters.
- The length of the ladder is the hypotenuse of the triangle.

### Step-by-step Solution:

1. **Identify the lengths of the legs of the triangle:**
- Height of the wall (vertical leg) = 60 m
- Distance from the wall to the base of the ladder (horizontal leg) = 11 m

2. **Apply the Pythagorean theorem:**
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
\[ c^2 = a^2 + b^2 \]
Here, let:
- \( a = 60 \) m (height of the wall)
- \( b = 11 \) m (distance from the wall)
- \( c \) = length of the ladder (what we need to find)

3. **Substitute the values into the equation:**
\[ c^2 = 60^2 + 11^2 \]

4. **Calculate the squares:**
\[ 60^2 = 3600 \]
\[ 11^2 = 121 \]

5. **Add the squares:**
\[ c^2 = 3600 + 121 = 3721 \]

6. **Take the square root to find the length of the ladder:**
\[ c = \sqrt{3721} \]
\[ c = 61 \text{ m} \]

### Conclusion:
The length of the ladder is **61 meters**.

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