SSC
Sample Paper
SSC CHSL (10+2) Sample Test Paper-21
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 \[=32\,+24=\underline{\mathbf{56}\,\mathbf{cm}}\]