The sides of a rectance are `(5.5 pm 0.1)` cm and `(3.5 pm 0.2)` cm . Its perimeter is

Options

A. `(18.0 pm 0.1)cm`
B. `(18.0 pm 0.2)cm`
C. `(18.0 pm 0.3)cm`
D. `(18.0 pm 0.6)cm`

Answer

To find the perimeter of a rectangle with given side lengths and their uncertainties, we can follow these steps:

### Step 1: Identify the dimensions of the rectangle
The dimensions of the rectangle are given as:
- Length (L) = \(5.5 \pm 0.1\) cm
- Breadth (B) = \(3.5 \pm 0.2\) cm

### Step 2: Write the formula for the perimeter of a rectangle
The formula for the perimeter (P) of a rectangle is:
\[ P = 2 \times (L + B) \]

### Step 3: Calculate the nominal perimeter
First, we calculate the nominal values of the length and breadth:
\[ L + B = 5.5 \, \text{cm} + 3.5 \, \text{cm} = 9.0 \, \text{cm} \]
Now, substitute this into the perimeter formula:
\[ P = 2 \times 9.0 \, \text{cm} = 18.0 \, \text{cm} \]

### Step 4: Calculate the uncertainty in the perimeter
To find the uncertainty in the perimeter, we need to consider the uncertainties in the length and breadth. The total uncertainty in the perimeter can be calculated as follows:
\[ \Delta P = 2 \times (\Delta L + \Delta B) \]
Where:
- \(\Delta L = 0.1 \, \text{cm}\) (uncertainty in length)
- \(\Delta B = 0.2 \, \text{cm}\) (uncertainty in breadth)

Calculating the total uncertainty:
\[ \Delta P = 2 \times (0.1 \, \text{cm} + 0.2 \, \text{cm}) = 2 \times 0.3 \, \text{cm} = 0.6 \, \text{cm} \]

### Step 5: Combine the nominal perimeter and its uncertainty
Now we can express the final result for the perimeter with its uncertainty:
\[ P = 18.0 \pm 0.6 \, \text{cm} \]

### Final Answer
The perimeter of the rectangle is:
\[ P = 18.0 \pm 0.6 \, \text{cm} \]

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