If the area to be covered for TV telecast is doubles then height of transmitting antenna (TV tower) will have to be:

Options

A. Doubled
B. Halved
C. Quadrupled
D. 16 times

Answer

To solve the problem, we need to establish the relationship between the area to be covered for TV telecast and the height of the transmitting antenna (TV tower).

### Step-by-Step Solution:

1. **Understanding the relationship between area and distance**:
The distance \( d \) that a TV signal can cover is given by the formula:
\[ d = \sqrt{2rh} \]
where \( r \) is the radius of the coverage area and \( h \) is the height of the antenna.

2. **Relating area to distance**:
The area \( A \) covered by the signal can be expressed as:
\[ A = \pi r^2 \]
Since the area is proportional to the square of the distance, we can say:
\[ A \propto d^2 \]

3. **Establishing the proportionality**:
From the above relationships, we can derive that:
\[ A \propto h \]
This means that if the area \( A \) is doubled, the height \( h \) must also change in a specific way.

4. **Setting up the equation**:
Let \( A_1 \) be the original area and \( A_2 \) be the new area. If \( A_2 = 2A_1 \), we can express this in terms of height:
\[ \frac{A_1}{A_2} = \frac{h_1}{h_2} \]
Substituting \( A_2 = 2A_1 \):
\[ \frac{A_1}{2A_1} = \frac{h_1}{h_2} \]
This simplifies to:
\[ \frac{1}{2} = \frac{h_1}{h_2} \]

5. **Finding the new height**:
Rearranging gives us:
\[ h_2 = 2h_1 \]
This means the height of the transmitting antenna must be doubled.

### Conclusion:
Thus, if the area to be covered for TV telecast is doubled, the height of the transmitting antenna (TV tower) will also have to be doubled.

### Final Answer:
The height of the transmitting antenna will have to be **doubled**.

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