If the height of TV tower is increased by `21%`, then the transmission range is enhanced by

Options

A. `10%`
B. `5%`
C. `15%`
D. `25%`

Answer

To solve the problem, we need to determine how the transmission range of a TV tower changes when its height is increased by 21%.

### Step-by-Step Solution:

1. **Understand the relationship between height and transmission range**:
The transmission range \( R \) of a TV tower is given by the formula:
\[ R \propto \sqrt{H} \]
where \( H \) is the height of the tower.

2. **Determine the new height after the increase**:
If the height of the tower is increased by 21%, the new height \( H' \) can be expressed as:
\[ H' = H + 0.21H = 1.21H \]

3. **Calculate the new transmission range**:
Since the range is proportional to the square root of the height, the new range \( R' \) can be expressed as:
\[ R' \propto \sqrt{H'} = \sqrt{1.21H} = \sqrt{1.21} \cdot \sqrt{H} \]
Thus, we can express the new range as:
\[ R' = \sqrt{1.21} \cdot R \]

4. **Calculate \( \sqrt{1.21} \)**:
We know that:
\[ \sqrt{1.21} = 1.1 \]
Therefore, the new range can be expressed as:
\[ R' = 1.1R \]

5. **Determine the percentage increase in transmission range**:
The percentage increase in the range can be calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{R' - R}{R} \right) \times 100\% \]
Substituting \( R' = 1.1R \):
\[ \text{Percentage Increase} = \left( \frac{1.1R - R}{R} \right) \times 100\% = \left( \frac{0.1R}{R} \right) \times 100\% = 10\% \]

### Final Answer:
The transmission range is enhanced by **10%**.