Question

If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to : 

A. 16 cm 

B. 15 cm 

C. 20 cm 

D. 17 cm

Answer 1

Option : (B)

ABCD is a rhombus 

AC = 18cm 

BD = 24cm 

We have to find the sides of the rhombus 

In triangle AOB, 

AO = 9cm (Diagonals of a parallelogram bisect each other) 

BO = 12cm 

AOB is a right - triangle right angled at O 

(Diagonals of a rhombus are perpendicular to each other) 

So, 

AB² = AO² + BO² (By Pythagoras theorem) 

AB² = 9² + 12² 

AB² = 81 + 144 

AB² = 225 

AB = 15cm 

In a rhombus, 

All sides are equal 

Thus, 

Each side of the rhombus is 15cm.