Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.

Let ABCD be the rhombus with diagonals AC and BD intersecting each other at O.
We know that the diagonals of a rhombus bisect each other at right angles.
∴">∴ If AC = 24 cm and BD =10 cm, AO = 12 cm and BO = 5 cm
Applying Pythagoras theorem in right-angled triangle AOB, we get:

$A B^{2}=A O^{2}+B O^{2}=12^{2}+5^{2}=144+25=169$

$A B=13 \mathrm{~cm}$

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