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Home » Pythagoras Triad Revealed: Why This Ancient Theorem Changed Math Forever! - Parker Core Knowledge

Pythagoras Triad Revealed: Why This Ancient Theorem Changed Math Forever! - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The sum of the first \( n \) natural numbers is \( \frac{n(n+1)}{2} \).

📌 Setting this equal to 55: \( \frac{n(n+1)}{2} = 55 \).

📌 Multiplying by 2: \( n(n+1) = 110 \).

📌 Solving \( n^2 + n - 110 = 0 \) using the quadratic formula, \( n = \frac{-1 \pm \sqrt{1 + 440}}{2} = \frac{-1 \pm 21}{2} \).

📌 Positive solution: \( n = 10 \).

📌 The perimeter of a rectangle is 60 meters, and its length is 5 meters more than twice its width. What is the width?

📌 Let the width be \( w \). Then the length is \( 2w + 5 \).

📌 Perimeter = \( 2(\text{length} + \text{width}) = 60 \).

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