Question

If the diagonals of a rhombus are 12 cm and 16 cm, find the length of each side.

Answer 1

In rhombus ABCD, diagonals AC and BD bisect each other at O at right angles.

AC= 16 cm. BD = 12 cm
$\therefore AO=OC=\frac{16}{2}=8cm$
$BO=OD=\frac{12}{2}=6cm$
$BO=OD=\frac{12}{2}=6cm$
Now, in right angled $\Delta AOB$,
$A{B}^2=A{O}^2+B{O}^2$
=$(8{)}^2+(6{)}^2=64+36=100=(10{)}^2$
$\therefore AB=10cm$
$\therefore$ Each side of rhombus = 10 cm