| In figure, \[\left. DE \right\|BC,\] \[\text{AD}=\text{1 cm}\] and \[\text{BD}=\text{2 cm}\]. The ratio of the \[ar(\Delta ABC)\]to the \[ar(\Delta ADE)\] is : |
 |
A) \[1:9\]
B) \[9:1\]
C) \[1:2\]
D) \[1:4\]
Correct Answer: B
Solution :
| [b] Given, \[AD=1\,cm,\] \[BD=2\,cm\] |
| and \[DE||BC.\] |
| In \[\Delta ABC\] and \[\Delta ADE.\] |
| \[\angle ABC=\angle ADE\] |
| (As \[DE||BC,\]so corresponding angles are equal) |
| \[\angle A=\angle A\] (Common angles) |
| \[\therefore \,\,\,\,\,\,\,\,\,\Delta ABC\tilde{\ }\Delta ADE,\] (By AA similarity) |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\frac{ar(\Delta ABC)}{ar(\Delta ADE)}=\frac{A{{B}^{2}}}{A{{D}^{2}}}={{\left( \frac{3}{1} \right)}^{2}}\] |
| \[[AB=AD+DB=1+2=3]\] |
| \[=\frac{9}{1}\] |
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