The diagonals of Rhombus 10 cm and 24 cm. Find the length of side of Rhombus.

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Solution

$\begin{matrix} G i v e n D i a g o n a l s o f a r b u s a r e 24 c m a n d 10 c m l e t A B C D b e a r b u s w i t h d i a g o n a l s A C = 10 c m a n d B D = 24 c m w e k n o w t h a t d i a g o n a l o f a r b u s b i sec t e a c h o t h e r a t 90^{\circ}, A O = O C & O B = O D & ∠ A O B = ∠ A O D = ∠ B O C = ∠ C O D = 90^{\circ} s o, A O = O C = 5 c m a n d B O = O D = 12 c m I n Δ A O B A B^{2} = O A^{2} + O B^{2} [B y u sin g p y t h a g o r a s t h e o r e m] A B^{2} = 5^{2} + 12^{2} A B^{2} = 25 + 144 A B^{2} = 169 ∴ A B = 13 c m H e n c e, t h e l e n g t h o f t h e e a c h s i d e o f t h e r b u s i s 13 c m . \end{matrix}$

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