Question

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

Answer 1

Let ABCD be the rhombus with diagonals (AC = 24 cm and BD = 10 cm) meeting at O.
We know that the diagonals of a rhombus bisect each other at angles.
Applying Pythagoras theorem in right-angled AOB, we get: 

`AB^2=AO^2+BO^2=12^2+5^2` 

`AB^2=144+25=169` 

`AB=sqrt169=13 cm` 

  

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