A) \[75\sqrt{3}\,sq.\,cm.\]
B) \[25\sqrt{3}\,sq.\,cm.\]
C) \[80\,sq.\,cm.\]
D) \[160\,sq.\,cm.\]
Correct Answer: C
Solution :
The diagonals of a rhombus-bisect each other at right angles. \[\therefore \]\[\angle AOB={{90}^{o}}:AO=OC:OD=OB\] If \[AC=2x\,cm.\,BD=x\,cm.\] In \[\Delta \Alpha {\mathrm O}\Beta \] \[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}\] \[\Rightarrow \]\[{{10}^{2}}={{x}^{2}}+{{\left( \frac{x}{2} \right)}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}+\frac{{{x}^{2}}}{4}=100\] \[\Rightarrow \]\[\frac{5{{x}^{2}}4}{4}=100\] \[\Rightarrow \]\[{{x}^{2}}=\frac{100\times 4}{5}=80\] ? (i) \[\therefore \]Area of rhombus \[=\frac{1}{2}\times {{d}_{1}}\times {{d}_{2}}\] \[=\frac{1}{2}\times 2x\times x\] \[={{x}^{2}}=80\,sq.\,cm.\]You need to login to perform this action.
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