The area of a square and a rectangle are equal. If side of the square is 50 cm and breadth of the rectangle is 30 cm. Find :
(i) Length of the rectangle.
(ii) Perimeter of the rectangle.

Options

A. (i)- 80 cm, (ii) 225 cm
B. (i) - 83.3 cm, (ii) - 226.6 cm
C. (i) 89.2 cm, (ii) - 226.6 cm
D. (i)-75.5 cm, (ii) 225.5 cm

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the area of the square.
The area of a square is given by the formula:
\[ \text{Area} = \text{side} \times \text{side} \]
Given that the side of the square is 50 cm:
\[ \text{Area of square} = 50 \, \text{cm} \times 50 \, \text{cm} = 2500 \, \text{cm}^2 \]

### Step 2: Set the area of the rectangle equal to the area of the square.
Since the area of the rectangle is equal to the area of the square:
\[ \text{Area of rectangle} = \text{Area of square} = 2500 \, \text{cm}^2 \]

### Step 3: Use the area of the rectangle to find the length.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{length} \times \text{breadth} \]
We know the breadth of the rectangle is 30 cm. Let \( L \) be the length of the rectangle. Therefore:
\[ L \times 30 \, \text{cm} = 2500 \, \text{cm}^2 \]
To find \( L \), we rearrange the equation:
\[ L = \frac{2500 \, \text{cm}^2}{30 \, \text{cm}} \]
Calculating this gives:
\[ L = \frac{2500}{30} \approx 83.33 \, \text{cm} \]

### Step 4: Calculate the perimeter of the rectangle.
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (L + B) \]
Substituting the values of \( L \) and \( B \):
\[ P = 2 \times (83.33 \, \text{cm} + 30 \, \text{cm}) \]
Calculating this gives:
\[ P = 2 \times 113.33 \, \text{cm} \approx 226.66 \, \text{cm} \]

### Final Answers:
(i) Length of the rectangle: \( \approx 83.33 \, \text{cm} \)
(ii) Perimeter of the rectangle: \( \approx 226.66 \, \text{cm} \)

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