A) \[9\,\text{cm}\]
B) \[10\,\text{cm}\]
C) \[8\,\text{cm}\]
D) \[20\,\text{cm}\]
Correct Answer: B
Solution :
[b] We know that, the diagonals of a rhombus are perpendicular bisectors of each other. |
Let ABCD be the rhombus such that, \[AC=16cm\] |
and \[BD=12cm\] |
\[\therefore \,\,\,\,\,\,\,\,\,\,\,AO=8cm,\] |
\[BO=6\,cm\] and \[\angle AOB=90{}^\circ \] |
In right angled \[\Delta AOB,\] |
\[A{{B}^{2}}=A{{O}^{2}}+O{{B}^{2}}\] (By Pythagoras theorem) |
\[\Rightarrow \,\,\,\,\,\,\,\,A{{B}^{2}}={{8}^{2}}+{{6}^{2}}=64+36=100\] |
\[\therefore \,\,\,\,\,\,\,\,\,\,\,AB=10cm\] |
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