The diagonal of a rhombus are of lengths 24 cm and 32 cm the side of rhombus (in cm) is

The diagonals of a rhombus bisect each other at right angles. So the half-diagonals are 12 cm and 16 cm, and each side of the rhombus is the hypotenuse of a right-angled triangle with these two legs.

Side = √(12² + 16²) = √(144 + 256) = √400 = 20 cm. So option B is correct.

• A) 16: This is only half of the longer diagonal, one leg of the triangle, not the side.
• C) 24: This is the full length of the shorter diagonal. A side cannot be read off a diagonal directly; the right triangle gives 20.
• D) 30: Check it: for 30 to be the side, 12² + 16² would have to equal 900. It is 400, so this is impossible.

The concept is simple: a rhombus has equal sides and diagonals that bisect each other at right angles, so every problem reduces to a right triangle and Pythagoras. This is standard Quantitative Aptitude and mensuration material in the CSAT paper, and the same half-diagonal method gives the area as half the product of the diagonals.

Trap: Forgetting to halve the diagonals before applying Pythagoras, which leads to a wrong hypotenuse.