If the diagonals of a rhombus are 8 cm and 6 cm, find its perimeter.

Let ABCD be a rhombus with AC and BD as two diagonals.

Let AC = 8 cm and BD = 6 cm.

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

∴ AO = 4 cm and BO = 3 cm.

In right angle triangle AOB,

Using Pythagoras theorem

⇒ AB² = AO² + BO²

⇒ AB² = 4² + 3²

⇒ AB² = 16 + 9 = 25

⇒ AB = $\sqrt{25}$ = 5 cm.

Side of rhombus ABCD = 5 cm

By formula,

Perimeter of rhombus = 4 × side = 4 × 5 = 20 cm.

Hence, perimeter of rhombus = 20 cm.