Question

The length of the diagonals PR and SQ of a rhombus are 8 cm and 6 cm PR respectively. Find the length of each side of the rhombus.​

Answer 1

Answer:

Given - PQRS is a rhombus and we know that all four sides of a rhombus are of equal length. 

And, In Δ POQ 

PQ is hypotenuse, OP is base and OQ is perpendicular.

Using Pythagoras Theorem -

⇒ (PQ)² = (OP)² + (OQ)²

⇒ (PQ)² = (3)² + (4)²

⇒ (PQ)² = 9 + 16

⇒ (PQ)² = 25

⇒ PQ = √25

⇒ PQ = 5 cm

So, length of each side of the given rhombus is 5 cm.

Perimeter of rhombus = 4 × side 

⇒ 4 × 5

= 20 cm

So, perimeter of the rhombus PQRS is 20 cm

Answer 2

Answer:

They form right angled triangles measuring 4cm and 3 cm (diagonals of rhombus bisect each other)

So length=

a²+b²=c²

4²+3²=c²

16+9=c²

25=c²

c=√25=5

Perimeter= 5 x 4 (all sides equal+

               =20cm

Hope its helpful :)