Median

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In triangle $ABC$, $AB = 7$, $AC = 15$, and the length of median $AM$ is $7$. Find the area of triangle $ABC$.

falafronk Mar 18, 2024

jilin73 · Answer 1 · 2024-03-18T06:36:04

Using Stewart's theorem, you can find that BM and CM are both √37 and not 4√2, which means our third side (BC) is of length 2√37 (= √148)

Then, using Heron's formula given by:

$16| \triangle ABC|^2 = 2a^2b^2+2b^2c^2+2c^2a^2-a^4-b^4-c^4$

you can calculate the area to be equal to exactly 42