If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to [1]a) 20 cm b) 15 cmc) 16 cm d) 17 cm

The diagonals of a rhombus bisect each other at right angles. Therefore, we can use the Pythagorean theorem to find the length of the side of the rhombus.

Step 1: Divide each diagonal by 2. We get 9 cm and 12 cm.

Step 2: Apply the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. We can write this as: a² = b² + c²

Here, the side of the rhombus is the hypotenuse, and the half-diagonals are the other two sides. Let's denote the side of the rhombus as a, half of one diagonal as b, and half of the other diagonal as c.

So, a² = b² + c² => a² = 9² + 12² => a² = 81 + 144 => a² = 225 => a = √225 => a = 15

So, the side of the rhombus is 15 cm. Therefore, the correct answer is (b) 15 cm.