Question

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

Answer 1

(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.