Perimeter of a square is 44 cm. The perimeter of a rectangle is equal to the perimeter of this square. The length of the rectangle is 5 cm more than the side of the square. The sum of areas (in `cm^(2)`) of the square and the rectangle is

Options

A. 217
B. 229
C. 169
D. 140

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Find the side length of the square.
The perimeter of a square is given by the formula:
\[ P = 4 \times \text{side} \]
Given that the perimeter of the square is 44 cm, we can set up the equation:
\[ 4 \times \text{side} = 44 \]
To find the side length, divide both sides by 4:
\[ \text{side} = \frac{44}{4} = 11 \text{ cm} \]

### Step 2: Calculate the area of the square.
The area \( A \) of a square is given by:
\[ A = \text{side}^2 \]
Substituting the value of the side we found:
\[ A = 11^2 = 121 \text{ cm}^2 \]

### Step 3: Determine the perimeter of the rectangle.
Since the perimeter of the rectangle is equal to the perimeter of the square, it is also 44 cm. The perimeter of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{breadth}) \]
Let the breadth of the rectangle be \( b \) and the length be \( l \). Thus:
\[ 2 \times (l + b) = 44 \]
Dividing both sides by 2:
\[ l + b = 22 \]

### Step 4: Find the length of the rectangle.
According to the problem, the length of the rectangle is 5 cm more than the side of the square:
\[ l = \text{side} + 5 = 11 + 5 = 16 \text{ cm} \]

### Step 5: Calculate the breadth of the rectangle.
Using the equation from Step 3:
\[ l + b = 22 \]
Substituting the length we found:
\[ 16 + b = 22 \]
To find \( b \), subtract 16 from both sides:
\[ b = 22 - 16 = 6 \text{ cm} \]

### Step 6: Calculate the area of the rectangle.
The area \( A \) of a rectangle is given by:
\[ A = l \times b \]
Substituting the values of length and breadth:
\[ A = 16 \times 6 = 96 \text{ cm}^2 \]

### Step 7: Find the sum of the areas of the square and the rectangle.
Now, we can find the total area:
\[ \text{Total Area} = \text{Area of Square} + \text{Area of Rectangle} \]
\[ \text{Total Area} = 121 + 96 = 217 \text{ cm}^2 \]

### Final Answer:
The sum of the areas of the square and the rectangle is **217 cm²**.

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