# What is the perimeter of a rhombus whose diagonals are 16 cm and 30 cm?

A rhombus has four equal sides.

## Answer: The perimeter of a rhombus whose diagonals are 16 cm and 30 cm is 68 cm.

Let's find the side of the rhombus first and then the perimeter.

**Explanation:**

Let's draw a diagram of the rhombus with the diagonals 16 cm and 30 cm

So AC = 30 cm and BD = 16 cm

Therefore, AO = 15 cm and BO = 8 cm

Now to find the perimeter, we need the length of AB.

Let's find AB using the pythagoras theorem in △AOB,

AB^{2 }= AO^{2 }+ OB^{2}

AB^{2 }= 15^{2 }+ 8^{2}

AB^{2 }= 225 + 64

AB^{2 }= 289

AB = √289

AB = 17 cm

Therefore, the length of one side of the rhombus is AB = 17 cm.

The Perimeter of the rhombus: P = 4 × length of the side

P = 4 × 17 cm

P = 68 cm

### Thus, the perimeter of a rhombus whose diagonals are 16 and 30 is 68 cm.

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