Multiple choice

The sides of a triangle ABC are 6, 7, 8, the smallest angle being C, then (b) the length of the median from C is

  1. $\sqrt{ \dfrac{95}{1} }$
  2. $\sqrt{ \dfrac{95}{2} }$
  3. $\sqrt{ \dfrac{95}{3} }$

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

By Apollonius's theorem, the length of the median from a vertex is given by the formula m = 0.5 times the square root of (2a squared + 2b squared - c squared). Since C is the smallest angle, side c = 6, while sides a = 7 and b = 8, allowing us to set up the equation m = 0.5 times the square root of (2(7 squared) + 2(8 squared) - 6 squared). Calculating the values gives m = 0.5 times the square root of (98 + 128 - 36), which simplifies to 0.5 times the square root of 190, or the square root of 190/4, but matching the options requires using m = the square root of (a squared + b squared)/2 - c squared/4, which results in the square root of 95/2.

Keep practicing — related questions