A) \[\text{25 c}{{\text{m}}^{\text{2}}}\]
B) \[\text{36 c}{{\text{m}}^{\text{2}}}\]
C) \[\text{6 c}{{\text{m}}^{\text{2}}}\]
D) \[\text{5 c}{{\text{m}}^{\text{2}}}\]
Correct Answer: B
Solution :
[b] In \[\Delta ADE\] and \[\Delta ABC,\] |
\[\angle DAE=\angle BAC\] (Common) |
\[\angle ADE=\angle ABC\] |
(Corresponding angles, as \[DE||BC\]) |
\[\therefore \,\,\,\,\Delta ADE\tilde{\ }\Delta ABC\](By AA similarity criterion) |
Since, ratio of areas of two similar triangles is equal to the square of the ratio of any two corresponding sides, |
\[\therefore \,\,\,\,\,\,\,\frac{ar(\Delta ADE)}{ar(\Delta ABC)}={{\left( \frac{DE}{BC} \right)}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\frac{ar(\Delta ADE)}{81}={{\left( \frac{\frac{2}{3}BC}{BC} \right)}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,ar(\Delta ADE)=\frac{4}{9}\times 81=36c{{m}^{2}}\] |
You need to login to perform this action.
You will be redirected in
3 sec