If diagonals of a rhombus are 16 cm and 30 cm. What is the perimeter (in cm) of the rhombus ?

Options

A. 32
B. 64
C. 34
D. 68

Answer

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

### Step 1: Understand the properties of a rhombus
A rhombus has four equal sides, and its diagonals bisect each other at right angles (90 degrees).

### Step 2: Identify the lengths of the diagonals
Given diagonals are:
- AC = 16 cm
- BD = 30 cm

### Step 3: Find half the lengths of the diagonals
Since the diagonals bisect each other:
- AO = OC = AC/2 = 16 cm / 2 = 8 cm
- BO = OD = BD/2 = 30 cm / 2 = 15 cm

### Step 4: Use the Pythagorean theorem to find the length of a side of the rhombus
In triangle AOB (formed by the diagonals), we can use the Pythagorean theorem:
- AB² = AO² + BO²
- AB² = 8² + 15²
- AB² = 64 + 225
- AB² = 289
- AB = √289
- AB = 17 cm

### Step 5: Calculate the perimeter of the rhombus
The perimeter (P) of a rhombus is given by:
- P = 4 × side length
- P = 4 × AB
- P = 4 × 17 cm
- P = 68 cm

### Final Answer
The perimeter of the rhombus is **68 cm**.

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