The lengths of the two diagonals of a rhombus are 6 cm and 8 cm. Find the length of its perimeter (in cm).

Options

A. 20
B. 10
C. 40
D. 30

Answer

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

### Step 1: Identify the lengths of the diagonals
Let the lengths of the diagonals be:
- AC = 6 cm
- BD = 8 cm

### Step 2: Calculate the half-lengths of the diagonals
Since the diagonals of a rhombus bisect each other at right angles, we can find the lengths of the segments formed by the intersection point (let's call it O):
- AO = AC / 2 = 6 cm / 2 = 3 cm
- BO = BD / 2 = 8 cm / 2 = 4 cm

### Step 3: Use the Pythagorean theorem to find the length of a side of the rhombus
In triangle AOB, we can apply the Pythagorean theorem:
- AB² = AO² + BO²
- AB² = (3 cm)² + (4 cm)²
- AB² = 9 cm² + 16 cm²
- AB² = 25 cm²
- AB = √25 cm² = 5 cm

### Step 4: Calculate the perimeter of the rhombus
The perimeter P of a rhombus is given by the formula:
- P = 4 × side length
- P = 4 × AB
- P = 4 × 5 cm = 20 cm

### Final Answer
The perimeter of the rhombus is 20 cm.

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