The lengths of the diagonals of a rhombus are 40 cm and 42 cm. Find the length of each side of the rhombus.

The diagonals of a rhombus bisect each other at right angles.

Let the intersecting point be O.

So, we get right angled triangles.

We know that the Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let us consider ΔAOB.

By Pythagoras Theorem,

AB² = AO² + OB²

AB² = 21² + 20²

AB² = 441 + 400

AB² = 841

AB = 29cm

The length of each side of the rhombus is 29cm.