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

 Mar 18, 2024
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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

 Mar 18, 2024

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