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Home » Solution: First, find the least common multiple of 12 and 18. - RTA

Solution: First, find the least common multiple of 12 and 18. - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Using Heron’s formula, $s = 12$, area $= \sqrt{12 \times 5 \times 4 \times 3} = 12\sqrt{5}$. The shortest altitude corresponds to the longest side (9): $h = \frac{2 \times 12\sqrt{5}}{9} = \frac{24\sqrt{5}}{9} = \frac{8\sqrt{5}}{3}$. \boxed{\dfrac{8\sqrt{5}}{3}}

📌 Final Refined Answer (with adjusted clarity):

📌 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 $s = \frac{7+8+9}{2} = 12$, and the area is $\sqrt{12 \times 5 \times 4 \times 3} = 12\sqrt{5}$. The altitude $h = \frac{2 \times \text{Area}}{9} = \frac{24\sqrt{5}}{9} = \boxed{\dfrac{8\sqrt{5}}{3}}$.

📌 Clarified Final Answer:

📌 For the triangle with sides 7, 8, 9, the shortest altitude (opposite side 9) is $\boxed{\dfrac{8\sqrt{5}}{3}}$.

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