The lengths of the diagonals of a rhombus are 30 cm and 40 cm. Find the side of the rhombus.

Answer

To find the side length of the rhombus given the lengths of its diagonals, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
The lengths of the diagonals are given as 30 cm and 40 cm.

2. **Label the diagonals**:
Let's denote the diagonals as AC and BD, where AC = 40 cm and BD = 30 cm.

3. **Find the midpoints of the diagonals**:
In a rhombus, the diagonals bisect each other at right angles. Let O be the intersection point of the diagonals. Therefore:
- AO = OC = AC/2 = 40 cm / 2 = 20 cm
- DO = OB = BD/2 = 30 cm / 2 = 15 cm

4. **Form a right triangle**:
We can now consider triangle OAB, where:
- OA = 20 cm (one half of diagonal AC)
- OB = 15 cm (one half of diagonal BD)

5. **Apply the Pythagorean theorem**:
According to the Pythagorean theorem, in triangle OAB:
\[ AB^2 = OA^2 + OB^2 \]
Substituting the values:
\[ AB^2 = 20^2 + 15^2 \]
\[ AB^2 = 400 + 225 \]
\[ AB^2 = 625 \]

6. **Calculate the length of the side**:
Taking the square root of both sides:
\[ AB = \sqrt{625} = 25 \text{ cm} \]

### Final Answer:
The length of each side of the rhombus is **25 cm**.

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