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Now substitute into $ f(x) $: - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 First, we calculate the area \( A \) of the triangle using Heron's formula. The semi-perimeter \( s \) is given by:

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

📌 The altitudes \( h_a \), \( h_b \), and \( h_c \) corresponding to sides \( a = 13 \), \( b = 14 \), and \( c = 15 \) are calculated as follows:

📌 h_a = \frac{2A}{a} = \frac{2 \times 84}{13} = \frac{168}{13} \approx 12.92

📌 h_b = \frac{2A}{b} = \frac{2 \times 84}{14} = 12

📌 h_c = \frac{2A}{c} = \frac{2 \times 84}{15} = \frac{168}{15} = 11.2

📌 The shortest altitude is \( h_c \), so:

📌 The hypotenuse of a right triangle is \( z \), and the radius of the inscribed circle is \( r \). Express the ratio of the area of the inscribed circle to the area of the triangle in terms of \( r \) and \( z \).

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