In triangle ABC, $AB = 12$ cm, $AC = 15$ cm and $BC = 18$ cm. Find the length of the median AD (in cm).
Answer and solution
Correct answer: A
Solution
D is the midpoint of BC, so $BD = 9$.
Apollonius' theorem: $AB^2 + AC^2 = 2(AD^2 + BD^2)$
$144 + 225 = 2(AD^2 + 81) \Rightarrow 369 = 2AD^2 + 162$
$AD^2 = 103.5 \Rightarrow AD = \sqrt{103.5}$ cm
Apollonius' theorem: $AB^2 + AC^2 = 2(AD^2 + BD^2)$
$144 + 225 = 2(AD^2 + 81) \Rightarrow 369 = 2AD^2 + 162$
$AD^2 = 103.5 \Rightarrow AD = \sqrt{103.5}$ cm