If each sides of a rhombus is 10 cm then what is the square root of sum of square of its diagonals ?

Options

A. A)`10sqrt(10)"cm"`
B. B)20 cm
C. C)`10sqrt(20)"cm"`
D. D)`20sqrt(10)"cm"`

Answer

To find the square root of the sum of the squares of the diagonals of a rhombus with each side measuring 10 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of a rhombus**:
In a rhombus, all four sides are equal, and the diagonals bisect each other at right angles.

2. **Identify the side length**:
Given that each side of the rhombus is 10 cm, we denote the side length as \( a = 10 \) cm.

3. **Use the property of the diagonals**:
The property of a rhombus states that the sum of the squares of the diagonals \( D_1 \) and \( D_2 \) is equal to four times the square of the side length:
\[ D_1^2 + D_2^2 = 4a^2 \]

4. **Calculate \( 4a^2 \)**:
Substitute \( a = 10 \) cm into the equation:
\[ 4a^2 = 4 \times (10)^2 = 4 \times 100 = 400 \]

5. **Find the square root of the sum of the squares of the diagonals**:
We need to find the square root of the value calculated in the previous step:
\[ \sqrt{D_1^2 + D_2^2} = \sqrt{400} = 20 \text{ cm} \]

6. **Conclusion**:
The square root of the sum of the squares of the diagonals of the rhombus is \( 20 \) cm.