Question

The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively. Find the length of each of its sides.

Answer 1

Let ABCD is a rhombus AC and BD are its diagonals which bisect each other at right angles at O.

AC= 16 cm and BD = 12 cm

$\therefore AO=\frac{16}{2}=8cm$

$BO=\frac{12}{2}=6cm$

Now, in right $△AOB$

$A{B}^2=A{O}^2+B{O}^2$ (Pythagoras Theorem)

=$(8{)}^2+(6{)}^2$

$=64+36=100=(10{)}^2$

$\therefore AB=10cm$

But all the sides of a rhombus are equal

$\therefore AB=10cm$