Question

the diagonals of rhombus is 20 cm and 21cm find the side of rhombus and its perimeter

Answer 1

As the diagonals of rhombus bisects each other by 90°

Then

By Pythagoras theorem,

(20/2)²+(21/2)²=side²

10²+(21/2)²=side²

100+441/4 =side²

(400+441)/4=side²

841/4 =side²

√{841/4} =side

29/2 =side

Then

Perimeter =4*side

Perimeter =4*29/2

Perimeter =2*29

Perimeter =58cm

Answer 2

Answer:

Side of the rhombus is 14.5 centimeter.

Perimeter of rhombus = 58 centimeters

Step-by-step explanation:

Since the diagonals of a rhombus bisect each other at right angles.

Therefore, applying Pythagoras theorem in the triangle formed by the intersection of the diagonals :

Side² = 10² + 10.5²

⇒ Side² = 100 + 110.25

⇒ Side² = 210.25

⇒ Side = 14.5

Hence, Side of the rhombus is 14.5 centimeter.

Perimeter of rhombus = 4 × side

                                     = 4 × 14.5

                                     = 58 centimeters