Question

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of the rhombus is 

A. 8 cm 

B. 9 cm 

C. 10 cm 

D. 12 cm

Answer 1

Let ABCD be a rhombus with diagonals AC and BD. 

AC and BD bisect at O.

So, AO = \(\frac{16}{2}\) = 8 cm

And BO = \(\frac{12}{2}\) = 6 cm

In right angled triangle AOB,

AB² = AO² + OB² (According to Pythagoras theorem)

AB² = 8² + 6²

AB² = 64 + 36

AB = \(\sqrt{100}\)

= 10 cm. 

So, Length of Rhombus of each side is 10 cm.