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ABC is a right angled triangle with a right angle at A. Points D, E are the middle points of AB and AC respectively. Which of the following relations is correct ?
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- 3(BE² + CD²) = 4BC²
- 4(BE² + CD²) = 5BC²
- 4(BE² + CD²) = 3BC²
- None of these
- 3(BE² + CD²) = 4BC²
Correct Option: B
According to question , we draw a figure of a right angled triangle ABC
Using Pythagoras theorem.
BE² = AE² + AB²
CD² = AC² + AD²
∴ BE² + CD² = AE² + AD² + AB² + AC²
| BE² + CD² = |  |  | ² | + | | | ² | + AB² + AC² | ||
| 2 | 2 |
| BE² + CD² = | + | + AB² + AC² | ||
| 4 | 4 |
⇒ 4 (BE² + CD²) = 5 (AB² + AC²) = 5BC²
