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, 

AD² = AO² + DO²

AD² = 8² + 15²

AD² = 64 + 225

AD² = 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.

☛ Check: NCERT Solutions for Class 7 Maths Chapter 6

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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.

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