| In \[\Delta ABC,\] \[\left. DE \right\|BC.\] If \[DE=4cm,\] \[BC=8cm\]and area of \[\Delta ADE=25c{{m}^{2}},\]then the area of \[\Delta ABC\]is: |
 |
A) \[50\,c{{m}^{2}}\]
B) \[100\,c{{m}^{2}}\]
C) \[75\,c{{m}^{2}}\]
D) None of the above
Correct Answer: B
Solution :
| [b] In \[\Delta ABC,\] \[DE||BC\] |
| \[\therefore \,\,\,\,\,\,\,\frac{ar(\Delta ADE)}{ar(\Delta ABC)}=\frac{{{(DE)}^{2}}}{{{(BC)}^{2}}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\frac{25}{ar(\Delta ABC)}=\frac{{{(4)}^{2}}}{{{(8)}^{2}}}=\frac{16}{64}=\frac{1}{4}\] |
| \[\therefore \,\,\,\,\,\,\,ar(\Delta ABC)=25\times 4=100\,c{{m}^{2}}\] |
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