The diagonals of a rhombus are 32 cm and 24 cm respectively. The perimeters of the rhombus is:

Options

A. 80 cm
B. 72 cm
C. 68 cm
D. 64 cm

Answer

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

### Step 1: Identify the lengths of the diagonals
The diagonals of the rhombus are given as:
- Diagonal AC = 32 cm
- Diagonal BD = 24 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 half-lengths of the diagonals:
- AO = AC/2 = 32 cm / 2 = 16 cm
- BO = BD/2 = 24 cm / 2 = 12 cm

### Step 3: Use the Pythagorean theorem to find the length of a side
In triangle AOB, we can use the Pythagorean theorem to find the length of side AB (which is the same as any side of the rhombus):
- AB² = AO² + BO²
- AB² = (16 cm)² + (12 cm)²
- AB² = 256 cm² + 144 cm²
- AB² = 400 cm²
- AB = √400 cm² = 20 cm

### Step 4: Calculate the perimeter of the rhombus
The perimeter (P) of a rhombus is given by the formula:
- P = 4 × side
- P = 4 × AB
- P = 4 × 20 cm = 80 cm

Thus, the perimeter of the rhombus is **80 cm**.