Q67 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics
In a triangle ABC , if $\mathrm{BC}=5, \mathrm{CA}=6, \mathrm{AB}=7$, then the length of the median drawn from B onto AC is
- A5
- B$7 \sqrt{5}$
- C$7 \sqrt{2}$
- Correct answerD$2 \sqrt{7}$
Solution
$b=6, c=7, a=5$
Median from B onto $\mathrm{AC}=\sqrt{\frac{2 a^2+2 c^2-b^2}{4}}$ $=\sqrt{\frac{2 \times 25+2 \times 49-36}{4}}=2 \sqrt{7}$
Median from B onto $\mathrm{AC}=\sqrt{\frac{2 a^2+2 c^2-b^2}{4}}$ $=\sqrt{\frac{2 \times 25+2 \times 49-36}{4}}=2 \sqrt{7}$
Hence, the correct answer is option: 'D'.