The area and the breadth of a rectangle are 288 `cm^(2)` and 16 cm respectively. Find the length of its perimeter (in cm).

Options

A. 34
B. 68
C. 136
D. 102

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Understand the given information
We are given:
- Area of the rectangle = 288 cm²
- Breadth of the rectangle = 16 cm

### Step 2: Use the formula for the area of a rectangle
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

### Step 3: Substitute the known values into the formula
We can rearrange the formula to find the length:
\[ \text{Length} = \frac{\text{Area}}{\text{Breadth}} \]
Substituting the known values:
\[ \text{Length} = \frac{288 \, \text{cm}^2}{16 \, \text{cm}} \]

### Step 4: Calculate the length
Now we perform the division:
\[ \text{Length} = \frac{288}{16} = 18 \, \text{cm} \]

### Step 5: Use the formula for the perimeter of a rectangle
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]

### Step 6: Substitute the values of length and breadth into the perimeter formula
Now we substitute the values we found:
\[ P = 2 \times (18 \, \text{cm} + 16 \, \text{cm}) \]

### Step 7: Calculate the perimeter
First, we calculate the sum inside the parentheses:
\[ 18 + 16 = 34 \, \text{cm} \]
Now we multiply by 2:
\[ P = 2 \times 34 = 68 \, \text{cm} \]

### Final Answer
The perimeter of the rectangle is **68 cm**.

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