Question

The lengths of the diagonals of a rhombus are 24cm and 10cm. The length of each side of the rhombus is 

(a) 12cm 

(b) 13cm 

(c) 14cm 

(d) 17cm

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: 

AB² = AO² + BO² = 12² + 5² 

= 144 + 25 = 169 

AB = \(\sqrt{169}\) = 13 

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