-
ABC is a right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B' and A'. The ratio of the area of the quadrilateral AA' B'B to the area of the triangle ABC is
-
- 1 : 2
- 2 : 3
- 3 : 4
- None of the above
- 1 : 2
Correct Option: C
A'B'C ~ ∆ABC
∠C = ∆C,
| = | and | = | ||||
| CA | 2 | CB | 2 |
and
| ∴ | = | = | |||
| ∆A'B'C | x² | 1 |
[ ∵ BC = 2B'C and AC = 2A'C]
| ⇒ | = | ||
| ∆ABC | 4 |
| ⇒ 1 - | = 1 - | ||
| ∆ABC | 4 |
| ⇒ | = | = 3 : 4 | ||
| ∆ABC | 4 |
