For a triangular microbial community with sides 7, 8, and 9 units, the shortest altitude is opposite the longest side (9 units). Using Heron’s formula, the semi-perimeter is $s = \frac7+8+92 = 12$, and the area is $\sqrt12 \times 5 \times 4 \times 3 = 12\sqrt5$. The altitude $h = \frac2 \times \textArea9 = \frac24\sqrt59 = \boxed\dfrac8\sqrt53$. - Crosslake
Mar 01, 2026
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