In a triangle ABC , if $\mathrm{BC}=5, \mathrm{CA}=6, \mathrm{AB}=7$, then the length of the median drawn…

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
  1. 5
  2. $7 \sqrt{5}$
  3. $7 \sqrt{2}$
  4. $2 \sqrt{7}$

Solution

$b=6, c=7, a=5$
Median from B onto $\mathrm{AC}=\sqrt{\frac{2 a^2+2 c^2-b^2}{4}}$ $=\sqrt{\frac{2 \times 25+2 \times 49-36}{4}}=2 \sqrt{7}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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