A horse is tied to a post by a rop. If the horse moves along a circular path always keeping the rope stretched and describes 88 metres when it as traced out `72^(@)` at the centre, the length of the rope is
(take `pi = (22)/(7)`)

Options

A. 70 m
B. 75 m
C. 80 m
D. 65 m

Answer

To find the length of the rope, we can use the relationship between the arc length, the angle subtended at the center, and the radius of the circular path.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The horse describes an arc length (s) of 88 meters.
- The angle subtended at the center (θ) is 72 degrees.
- We need to find the length of the rope (which is the radius, r).

2. **Use the Arc Length Formula**:
The formula for the arc length is given by:
\[ s = \frac{\theta}{360} \times 2\pi r \]
where:
- \( s \) = arc length
- \( \theta \) = angle in degrees
- \( r \) = radius (length of the rope)

3. **Substitute the Known Values**:
Substitute \( s = 88 \) meters and \( \theta = 72 \) degrees into the formula:
\[ 88 = \frac{72}{360} \times 2 \times \frac{22}{7} \times r \]

4. **Simplify the Equation**:
First, simplify \( \frac{72}{360} \):
\[ \frac{72}{360} = \frac{1}{5} \]
So the equation becomes:
\[ 88 = \frac{1}{5} \times 2 \times \frac{22}{7} \times r \]
Now, calculate \( \frac{1}{5} \times 2 = \frac{2}{5} \):
\[ 88 = \frac{2}{5} \times \frac{22}{7} \times r \]

5. **Multiply and Rearrange**:
Multiply both sides by 5 to eliminate the fraction:
\[ 440 = 2 \times \frac{22}{7} \times r \]
Now, calculate \( 2 \times \frac{22}{7} = \frac{44}{7} \):
\[ 440 = \frac{44}{7} \times r \]

6. **Solve for r**:
To isolate \( r \), multiply both sides by \( \frac{7}{44} \):
\[ r = 440 \times \frac{7}{44} \]
Simplifying this gives:
\[ r = 10 \times 7 = 70 \text{ meters} \]

### Final Answer:
The length of the rope is **70 meters**.