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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