# The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

**Solution:**

Let us understand this problem better by drawing a rhombus with the given dimensions shown below.

Let ABCD be a rhombus, all sides of the rhombus have equal length and its diagonal AC and BD are intersecting each other at a point O.

As we know that the diagonals in the rhombus bisect each other at 90^{o}.

So, AO can be written as (AC/2)

= 16/2

= 8 cm

And, DO can be written as (BD/2)

= 30/2

= 15 cm

Then, consider the triangle AOD and apply Pythagoras theorem,

AD^{2} = AO^{2} + DO^{2}

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

AD^{2} = 64 + 225

AD^{2} = 289

AD = √289

AD = 17 cm

Hence, the length of each side of the rhombus is 17 cm

Now,

The perimeter of rhombus = 4 × side of the rhombus

= 4 × 17

= 68 cm

Therefore, the perimeter of the rhombus is 68 cm.

**Video solution:**

## The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

### Maths NCERT Solutions Class 7 - Chapter 6 Exercise 6.5 Question 8

**Summary:**

The diagonals of a rhombus measure 16 cm and 30 cm. The perimeter of the rhombus is 68 cm.