The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is

Options

A. 9 cm
B. 10 cm
C. 8 cm
D. 20 cm

Answer

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

### Step 1: Understand the properties of a rhombus
A rhombus has two important properties regarding its diagonals:
- The diagonals bisect each other at right angles (90 degrees).
- All sides of a rhombus are of equal length.

### Step 2: Identify the lengths of the diagonals
Given:
- Length of diagonal AC = 16 cm
- Length of diagonal BD = 12 cm

### Step 3: Find the lengths of the halves of the diagonals
Since the diagonals bisect each other, we can find the lengths of the segments formed by the intersection point O:
- AO = OC = AC / 2 = 16 cm / 2 = 8 cm
- BO = OD = BD / 2 = 12 cm / 2 = 6 cm

### Step 4: Use the Pythagorean theorem
In triangle AOB, we can apply the Pythagorean theorem since it is a right triangle:
- AO² + OB² = AB²
Where:
- AO = 8 cm
- OB = 6 cm
- AB = length of the side of the rhombus (let's denote it as X)

### Step 5: Substitute the values into the equation
Substituting the known values into the equation:
- (8 cm)² + (6 cm)² = X²
- 64 cm² + 36 cm² = X²
- 100 cm² = X²

### Step 6: Solve for X
To find the length of the side of the rhombus, take the square root of both sides:
- X = √(100 cm²)
- X = 10 cm

### Conclusion
The length of each side of the rhombus is **10 cm**.

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