Assertion : Breadth of the rectangle whose perimeter 160 cm and length 16 cm is 10 cm.
Reason : Perimeter of a rectangle = 2(length + breadth)

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to verify the assertion and reason given regarding the rectangle's dimensions.

### Step-by-Step Solution:

1. **Identify the given values:**
- Perimeter (P) = 160 cm
- Length (L) = 16 cm

2. **Recall the formula for the perimeter of a rectangle:**
\[ P = 2 \times (L + B) \]
where B is the breadth.

3. **Substitute the known values into the perimeter formula:**
\[ 160 = 2 \times (16 + B) \]

4. **Simplify the equation:**
- First, divide both sides by 2:
\[ 80 = 16 + B \]

5. **Isolate B (breadth) in the equation:**
\[ B = 80 - 16 \]
\[ B = 64 \text{ cm} \]

6. **Conclusion:**
- The calculated breadth is 64 cm, not 10 cm as stated in the assertion. Therefore, the assertion is false.

### Final Verification:
- The reason provided states that the perimeter formula is correct, which is true. Thus, the assertion is false, but the reason is true.

### Summary:
- Assertion: False (The breadth is not 10 cm; it is 64 cm)
- Reason: True (The perimeter formula is correct)