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Home » Multiply both sides by 2: \( n(n + 1) = 10100 \). - High Altitude Science

Multiply both sides by 2: \( n(n + 1) = 10100 \). - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The semiperimeter \(s\) is:

📌 s = \frac{a + b + c}{2}

📌 The inradius is related to area by:

📌 A = r \cdot s \quad \Rightarrow \quad r = \frac{A}{s}

📌 We want to compute \(\frac{A}{r^2}\):

📌 \frac{A}{r^2} = \frac{A}{\left(\frac{A}{s}\right)^2} = \frac{A \cdot s^2}{A^2} = \frac{s^2}{A}

📌 Now express \(A\) and \(s\) in terms of \(c\). For a right triangle:

📌 A = \frac{1}{2}ab, \quad \text{and} \quad a^2 + b^2 = c^2

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