| In the given figure, if \[DE\left\| BC, \right.\] \[\text{AE}=\text{8}\,\text{cm},\] \[\text{EC}=\text{2 cm}\] and \[\text{BC}=\text{6 cm},\]then DE is: (CBSE 2014) |
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A) \[\text{2}.\text{7 cm}\]
B) \[3.2\text{ cm}\]
C) \[4.4\text{ cm}\]
D) \[4.8\text{ cm}\]
Correct Answer: D
Solution :
| [d] In \[\Delta ADE\] and \[\Delta ABC,\] |
| \[\angle DAE=\angle BAC\] (Common angle) |
| \[\angle ADE=\angle ABC\] (Corresponding angles) |
| \[\therefore \,\,\Delta ADE\tilde{\ }\Delta ABC\] (By AA similarity) |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\frac{AE}{AC}=\frac{DE}{BC}\Rightarrow \frac{8}{8+2}=\frac{DE}{2}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\frac{8}{10}=\frac{DE}{6}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,DE=\frac{8\times 6}{10}=\frac{48}{10}=4.8\,\,cm\] |
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