InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
In ΔABC; D, E and F are the mid points of the sides, then ar(ΔDEF) =A) 1/3 ar(ΔABC) B) 1/2 ar(ΔABC) C) 1/4 ar(ΔABC) D) 3 ar(ΔABC) |
|
Answer» Correct option is (C) \(\frac{1}{4}ar(\triangle ABC)\) \(\because\) D, E and F are the mid-points of the sides AB, BC and AC respectively. \(\therefore\) DF = \(\frac12BC,\) FE \(=\frac12AB\) and DE \(=\frac12AC\) \(\Rightarrow\) \(\frac{DF}{BC}=\frac{1}{2},\frac{FE}{AB}=\frac{1}{2}\;and\;\frac{DE}{AC}=\frac{1}{2}\) \(\therefore\) \(\frac{FE}{AB}=\frac{DE}{AC}=\frac{DF}{BC}=\frac{1}{2}\) \(\therefore\) \(\frac{ar(\triangle DEF)}{ar(\triangle ABC)}=(\frac{DF}{BC})^2\) \(=(\frac12)^2=\frac14\) \(\therefore\) \(ar(\triangle DEF)=\) \(\frac{1}{4}ar\,(\triangle ABC)\) Correct option is C) 1/4 ar(ΔABC) |
|