Given the lengths of the diagonals of a rhombus are 30 cm and 40 cm.

Let the diagonals AC and BD of the rhombus ABCD meet at point O.

We know that the diagonals of the rhombus bisect each other perpendicularly.

Also we know that Pythagoras theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Consider right triangle AOD,

⇒ AD² = AO² + OD²

= 15² + 20²

= 225 + 400

= 625

⇒ AD = 25 cm

∴ The side of the rhombus is 25 cm.