Question

If one of the diagonals in a rhombus is 20 cm long and second is 10√6 cm , then find the side of the rhombus.​

Answer 1

Answer:

side = 5√10 cm

Step-by-step explanation:

We know that,

Diagonal of rhombus bisect each other at 90°.

1/2 d1. = 20 / 2 = 10cm

1/2 d2. = 10√6 / 2 = 5√6 cm

Using Pythagoras Theorem

=> side^2 = 1/2 d1^2 + 1/2 d2^2

=> side^2 = (10)^2 + (5√6)^2

=> side^2 = 100 + 150

=> side^2 = 250

=> side = √250 = 5√10 cm

Hope my answer helps you.

Answer 2

Given: The lengths of two diagonals of a rhombus = 20 cm and 10√6 cm

To find: The side of the rhombus

Solution: We know that,

Diagonals of a rhombus bisect each other at 90°.

Let the diagonals be d1 = 20 cm and d2 = 10√6 cm, and the side be x cm.

As such, 1/2 of d1 = 10 cm

1/2 of d2 = 5√6 cm

The half parts of the two diagonals form a right angled triangle with the side of the rhombus.

Hence using Pythagoras' Theorem,

x² = (1/2 of d1)² + (1/2 of d2)²

⇒ x² = (10)² + (5√6)²

⇒ x² = 100 + (25 × 6)

⇒ x² = 100 + 150

⇒ x² = 250

⇒ x = 5√10

Answer: The side of the rhombus is 5√10 cm.