The lengths of the diagonals of a rhombus are 24 cm and 10 cm. The length of each side of the rhombus is
(a) 12 cm
(b) 13 cm
(c) 14 cm
(d) 17 cm

(b) 13 cm

Let ABCD be the rhombus with diagonals AC and BD intersecting each other at O.
We have:
AC = 24 cm and BD = 10 cm
We know that diagonals of a rhombus bisect each other at right angles.
Therefore applying Pythagoras theorem in right-angled triangle AOB, we get:
$$\begin{gathered} A{B}^2 = A{O}^2 + B{O}^2 = {12}^2 + 5^2 \\ = 144 + 25 = 169 \\ AB = \sqrt{169} = 13 \end{gathered}$$

Hence, the length of each side of the rhombus is 13 cm.