In rhombus if diagonals are 30 cm and 40 cm, find its perimeter.

Let AC = 30 cm and BD = 40 cm.

We know that,

Diagonals of rhombus are perpendicular and bisect each other,

OB = $\dfrac{1}{2}BD$ = 20 cm and AO = $\dfrac{1}{2}$AC = 15 cm.

In right triangle AOB,

By pythagoras theorem we get,

⇒ AB² = AO² + OB²

⇒ AB² = 15² + 20²

⇒ AB² = 225 + 400

⇒ AB² = 625

⇒ AB = 25 cm.

Hence, each side of rhombus is 25 cm as all sides of rhombus are equal.

Perimeter = 4(Side) = 100 cm.

Hence, perimeter of rhombus = 100 cm.