Each side of a rhombus is 10 cm, the sum of square of its diagonal is

Options

A. A)20 `"cm"^(2)`
B. B)200 `"cm"^(2)`
C. C)400 `"cm"^(2)`
D. D)100 `"cm"^(2)`

Answer

To find the sum of the squares of the diagonals of a rhombus where each side is 10 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
- Each side of the rhombus (denoted as \( a \)) is 10 cm.

2. **Use the formula for the sum of the squares of the diagonals**:
- The formula for the sum of the squares of the diagonals \( D_1 \) and \( D_2 \) of a rhombus is:
\[ D_1^2 + D_2^2 = 4a^2 \]
where \( a \) is the length of a side of the rhombus.

3. **Substitute the value of \( a \)**:
- Since \( a = 10 \) cm, we substitute this value into the formula:
\[ D_1^2 + D_2^2 = 4 \times (10)^2 \]

4. **Calculate \( (10)^2 \)**:
- \( (10)^2 = 100 \)

5. **Multiply by 4**:
- Now, calculate \( 4 \times 100 \):
\[ D_1^2 + D_2^2 = 400 \]

6. **Final answer**:
- Therefore, the sum of the squares of the diagonals is:
\[ D_1^2 + D_2^2 = 400 \text{ cm}^2 \]