Study the given statements carefully and select the correct option.
Statement - I : If the side of a square is halved, then the new perimeter is two times the original perimeter.
Statement - II : If the perimeter of a regular pentagon is 35 cm, then the length of its each side is 5 cm.

Options

A. Both Statement-I and Statement-II are true.
B. Both Statement-I and Statement-II are false
C. Statement - I is true but Statement-II is false.
D. Statement-I is false but Statement-II is true.

Answer

To solve the problem, we need to analyze both statements provided and determine their validity.

### Statement I:
"If the side of a square is halved, then the new perimeter is two times the original perimeter."

1. **Calculate the original perimeter of the square:**
- Let the original side length of the square be \( S \).
- The formula for the perimeter \( P \) of a square is given by:
\[ P = 4 \times S \]

2. **Calculate the new side length:**
- If the side is halved, the new side length becomes:
\[ \text{New Side} = \frac{S}{2} \]

3. **Calculate the new perimeter:**
- The new perimeter \( P' \) is:
\[ P' = 4 \times \left(\frac{S}{2}\right) = 4 \times \frac{S}{2} = \frac{4S}{2} = 2S \]

4. **Compare the new perimeter with the original perimeter:**
- The original perimeter was \( 4S \) and the new perimeter is \( 2S \).
- Therefore, the new perimeter is not two times the original perimeter, but rather half of it:
\[ P' = 2S \quad \text{(which is half of } 4S\text{)} \]

**Conclusion for Statement I:**
- Statement I is **false**.

### Statement II:
"If the perimeter of a regular pentagon is 35 cm, then the length of each side is 5 cm."

1. **Understand the properties of a regular pentagon:**
- A regular pentagon has 5 equal sides.

2. **Let the length of each side be \( x \):**
- The perimeter \( P \) of the pentagon is given by:
\[ P = 5 \times x \]

3. **Set up the equation with the given perimeter:**
- We know the perimeter is 35 cm:
\[ 5x = 35 \]

4. **Solve for \( x \):**
- Divide both sides by 5:
\[ x = \frac{35}{5} = 7 \text{ cm} \]

**Conclusion for Statement II:**
- The length of each side is 7 cm, not 5 cm. Therefore, Statement II is also **false**.

### Final Conclusion:
Both statements are false.

### Summary of Steps:
1. Calculate the original perimeter of the square.
2. Determine the new side length after halving.
3. Calculate the new perimeter and compare it with the original.
4. Understand the properties of a regular pentagon.
5. Set up the equation for the perimeter and solve for the side length.