Two squares have sides x cm and `(2x+1)` cm, respectively. The sum of their perimeters is 100 cm. Area (in `cm^(2)`) of the bigger square is

Options

A. 225
B. 289
C. 64
D. 81

Answer

To find the area of the bigger square given the sides of two squares and the sum of their perimeters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the sides of the squares**:
- The side of the first square is given as \( x \) cm.
- The side of the second square is given as \( 2x + 1 \) cm.

2. **Calculate the perimeter of each square**:
- The perimeter \( P \) of a square is given by the formula \( P = 4 \times \text{side} \).
- For the first square:
\[ P_1 = 4x \]
- For the second square:
\[ P_2 = 4(2x + 1) = 8x + 4 \]

3. **Set up the equation for the sum of the perimeters**:
- According to the problem, the sum of the perimeters of both squares is 100 cm:
\[ P_1 + P_2 = 100 \]
- Substituting the expressions for the perimeters:
\[ 4x + (8x + 4) = 100 \]

4. **Simplify the equation**:
- Combine like terms:
\[ 12x + 4 = 100 \]

5. **Solve for \( x \)**:
- Subtract 4 from both sides:
\[ 12x = 96 \]
- Divide by 12:
\[ x = 8 \]

6. **Find the side of the second square**:
- Substitute \( x \) back into the expression for the side of the second square:
\[ \text{Side of second square} = 2x + 1 = 2(8) + 1 = 16 + 1 = 17 \text{ cm} \]

7. **Calculate the area of the bigger square**:
- The area \( A \) of a square is given by the formula \( A = \text{side}^2 \).
- For the bigger square:
\[ A = 17^2 = 289 \text{ cm}^2 \]

### Final Answer:
The area of the bigger square is \( 289 \text{ cm}^2 \).

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