question_answer

In a rhombus of side 20 cm, one of the diagonals is 24 cm long. Find the sum of both diagonals.

A)  60 cm                         

B)  56 cm

C)  68 cm                         

D)  54 cm

Correct Answer: B

Solution :

 Side of rhombus = 20 cm One of the diagonal = 24 cm             [\[\because \]  Rhombus diagonals a intersect each other at\[90{}^\circ \]] In \[\Delta \,DOC-\] \[{{(DC)}^{2}}={{(DO)}^{2}}+{{(CO)}^{2}}\Rightarrow 400\,\,\,144+{{(CO)}^{2}}\] \[CO=\sqrt{256}=16cm.\,\,\Rightarrow \,\,AC=2CO\] \[=2\times 16=32\,\,cm.\] The sum of both diagonals \[=32\,+24=\underline{\mathbf{56}\,\mathbf{cm}}\]