Assertion : The length of rectangle of area `135 cm^(2)` and breadth 9 cm is 15 cm.
Reason : Length of the rectangle = Area `xx` 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 evaluate the assertion and the reason provided regarding the rectangle's dimensions.

### Step 1: Understand the Assertion
The assertion states that the length of a rectangle with an area of \(135 \, \text{cm}^2\) and a breadth of \(9 \, \text{cm}\) is \(15 \, \text{cm}\).

### Step 2: Use the Area Formula
The area \(A\) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
We can rearrange this to find the length:
\[ \text{Length} = \frac{\text{Area}}{\text{Breadth}} \]

### Step 3: Substitute the Values
Now, we substitute the given values into the formula:
\[ \text{Length} = \frac{135 \, \text{cm}^2}{9 \, \text{cm}} \]

### Step 4: Perform the Calculation
Now, we perform the division:
\[ \text{Length} = \frac{135}{9} = 15 \, \text{cm} \]

### Step 5: Verify the Assertion
Since we calculated the length to be \(15 \, \text{cm}\), the assertion is correct.

### Step 6: Evaluate the Reason
The reason states that the length of the rectangle is equal to the area multiplied by the breadth. This is incorrect because the correct relationship is that the length is equal to the area divided by the breadth.

### Conclusion
- The assertion is **true**: The length is \(15 \, \text{cm}\).
- The reason is **false**: The relationship stated is incorrect.

### Final Answer
The correct option is that the assertion is true, but the reason is false.

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