A square and a rectangle have equal areas. If each side of the square is 18 cm and the width of the rectangle is 12 cm, then find the perimeter of the rectangle.

Options

A. 48cm
B. 56cm
C. 92cm
D. 78cm

Answer

To find the perimeter of the rectangle given that a square and a rectangle have equal areas, we can follow these steps:

### Step 1: Calculate the area of the square.
The area of a square is given by the formula:
\[ \text{Area of square} = \text{side} \times \text{side} \]
Given that each side of the square is 18 cm:
\[ \text{Area of square} = 18 \, \text{cm} \times 18 \, \text{cm} = 324 \, \text{cm}^2 \]

### Step 2: Set the area of the rectangle equal to the area of the square.
Since the areas of the square and rectangle are equal:
\[ \text{Area of rectangle} = \text{Area of square} = 324 \, \text{cm}^2 \]

### Step 3: Use the width of the rectangle to find its length.
The area of a rectangle is given by the formula:
\[ \text{Area of rectangle} = \text{length} \times \text{width} \]
Let the length of the rectangle be \( L \) and the width be \( B \). We know the width \( B = 12 \, \text{cm} \).
Thus,
\[ L \times 12 \, \text{cm} = 324 \, \text{cm}^2 \]

### Step 4: Solve for the length \( L \).
Rearranging the equation to find \( L \):
\[ L = \frac{324 \, \text{cm}^2}{12 \, \text{cm}} = 27 \, \text{cm} \]

### Step 5: 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 \( B \):
\[ P = 2 \times (27 \, \text{cm} + 12 \, \text{cm}) = 2 \times 39 \, \text{cm} = 78 \, \text{cm} \]

### Final Answer:
The perimeter of the rectangle is \( 78 \, \text{cm} \).

---