A rhombus has diagonals of length 8 cm and 6 cm. Find its perimeter.

Options

A. 24 cm
B. 28 cm
C. 18 cm
D. 20 cm

Answer

To find the perimeter of a rhombus with diagonals of lengths 8 cm and 6 cm, we can follow these steps:

### Step 1: Understand the properties of the rhombus
A rhombus has two diagonals that bisect each other at right angles. This means each diagonal divides the rhombus into four right-angled triangles.

### Step 2: Calculate the lengths of the half diagonals
Given the lengths of the diagonals:
- Diagonal 1 (d1) = 8 cm
- Diagonal 2 (d2) = 6 cm

Each diagonal is bisected, so:
- Half of diagonal 1 = 8 cm / 2 = 4 cm
- Half of diagonal 2 = 6 cm / 2 = 3 cm

### Step 3: Use the Pythagorean theorem to find the side length of the rhombus
In one of the right-angled triangles formed by the diagonals, we can denote:
- One leg (half of diagonal 1) = 4 cm
- Other leg (half of diagonal 2) = 3 cm
- Hypotenuse (the side of the rhombus) = s

According to the Pythagorean theorem:
\[ s^2 = (4 \text{ cm})^2 + (3 \text{ cm})^2 \]
\[ s^2 = 16 + 9 \]
\[ s^2 = 25 \]
\[ s = \sqrt{25} \]
\[ s = 5 \text{ cm} \]

### Step 4: Calculate the perimeter of the rhombus
The perimeter (P) of a rhombus is given by the formula:
\[ P = 4 \times s \]
Substituting the value of s:
\[ P = 4 \times 5 \text{ cm} \]
\[ P = 20 \text{ cm} \]

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

---