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Home » coulrophobia is the fear of - Redraw

coulrophobia is the fear of - Redraw

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \times 8 \times 7 \times 6}

📌 = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{7056}

📌 The altitudes \(h_a\), \(h_b\), \(h_c\) corresponding to sides \(a\), \(b\), \(c\) are given by:

📌 h_a = \frac{2A}{a}, \quad h_b = \frac{2A}{b}, \quad h_c = \frac{2A}{c}

📌 The shortest altitude corresponds to the longest side, which is \(c = 15\):

📌 h_{\text{min}} = \frac{2 \times 84}{15} = \frac{168}{15} = \frac{56}{5} = 11.2

📌 Thus, the length of the shortest altitude is \(\boxed{\frac{56}{5}}\) units.

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