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Home » Rachel Nichols Shocked Jimmy Butler—What He Said Next Will Blow Your Mind! - Crosslake

Rachel Nichols Shocked Jimmy Butler—What He Said Next Will Blow Your Mind! - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \boxed{1 - \frac{\sqrt{2}}{2}}

📌 Question: Find the length of the shortest altitude of a triangle with side lengths 13 cm, 14 cm, and 15 cm.

📌 Solution: First, compute the area using Heron’s formula. The semi-perimeter is:

📌 s = \frac{13 + 14 + 15}{2} = 21

📌 A = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6} = \sqrt{7056} = 84

📌 The altitude corresponding to side $a$ is given by $h_a = \frac{2A}{a}$. Compute each altitude:

📌 h_{13} = \frac{2 \cdot 84}{13} = \frac{168}{13}, \quad h_{14} = \frac{168}{14} = 12, \quad h_{15} = \frac{168}{15} = 11.2

📌 The shortest altitude is $11.2$.

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