| In the given figure, P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ is parallel to BC and divides the triangle ABC into two parts, equal in area. The ratio of \[\text{PA}:\text{AB}=\] |
 |
A) \[1:1\]
B) \[(\sqrt{2}-1):\sqrt{2}\]
C) \[1:\sqrt{2}\]
D) \[(\sqrt{2}-1):1\]
Correct Answer: C
Solution :
| [c] As PQ is parallel to BC |
| \[\Delta ABC\tilde{\ }\Delta APQ\] |
| \[\frac{Area\,\,of\,\Delta ABC}{Area\,\,of\,\Delta APQ}=\frac{2}{1}\] |
| Ratio of sides \[=\frac{AB}{AP}=\frac{\sqrt{2}}{1}\] |
| \[AP:AB=1:\sqrt{2}\] |
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