The area of a rectangle is 630 `cm^(2)` and its length is 35 cm. find the perimeter of the rectangle.

Options

A. 106 cm
B. 53 cm
C. 325 cm
D. 44 cm

Answer

To find the perimeter of the rectangle given its area and length, we can follow these steps:

### Step 1: Understand the formulas
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]

### Step 2: Identify the known values
From the question, we know:
- Area \( A = 630 \, \text{cm}^2 \)
- Length \( L = 35 \, \text{cm} \)

### Step 3: Find the breadth
We can rearrange the area formula to find the breadth \( B \):
\[ B = \frac{A}{L} \]
Substituting the known values:
\[ B = \frac{630 \, \text{cm}^2}{35 \, \text{cm}} \]

### Step 4: Calculate the breadth
Now, we perform the division:
\[ B = \frac{630}{35} \]
To simplify, we can divide both the numerator and the denominator by 7:
\[ B = \frac{630 \div 7}{35 \div 7} = \frac{90}{5} = 18 \, \text{cm} \]

### Step 5: Calculate the perimeter
Now that we have both the length and breadth, we can find the perimeter using the perimeter formula:
\[ P = 2 \times (L + B) \]
Substituting the values:
\[ P = 2 \times (35 \, \text{cm} + 18 \, \text{cm}) \]

### Step 6: Perform the addition
Calculate the sum inside the parentheses:
\[ P = 2 \times 53 \, \text{cm} \]

### Step 7: Calculate the final perimeter
Now, multiply by 2:
\[ P = 106 \, \text{cm} \]

Thus, the perimeter of the rectangle is **106 cm**.

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