The altitude corresponding to a side is given by \( h = \frac{2A}{\text{side}} \). We compute the altitudes for each side:
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- s = \frac{13 + 14 + 15}{2} = 21 \text{ m.}
- A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6}
- = \sqrt{21 \cdot 8 \cdot 7 \cdot 6} = \sqrt{7056} = 84 \text{ square meters.}
- For side 13 m: \( h_{13} = \frac{2 \cdot 84}{13} = \frac{168}{13} \approx 12.92 \) m
- For side 14 m: \( h_{14} = \frac{168}{14} = 12 \) m
- For side 15 m: \( h_{15} = \frac{168}{15} = 11.2 \) m
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