question_answer

The diagonals of a rhombus are 12 cm and 16 cm, respectively. The length of one side is

A) 8 cm

B) 6 cm

C) 10 cm

D) 12 cm

Correct Answer: C

Solution :

[c] \[{{d}_{1}}=12\,cm\] \[{{d}_{2}}=16\,cm\] \[\therefore \]      \[OA=\frac{1}{2}{{d}_{1}}=6\,cm\] and       \[OB=\frac{1}{2}{{d}_{2}}=8\,cm\] Now, in \[\Delta AOB,\] \[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}\] \[=36+64=140\] \[\Rightarrow \]   \[AB=10\,cm\]