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Home » Let the width of the rectangle be \( w \). - Midis

Let the width of the rectangle be \( w \). - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 2a - (3 + \sqrt{5})a + 2b + (3 + \sqrt{5})b = 0

📌 \Rightarrow a(-1 - \sqrt{5}) + b(5 + \sqrt{5}) = 0

📌 Solve for \( rac{a}{b} \):

📌 a b ( -\overline{1 + \sqrt{5}} + (5 + \sqrt{5}) ) = 0 \Rightarrow -rac{a}{b} - \sqrt{5} \cdot rac{a}{b} + 5 + \sqrt{5} = 0

📌 Let \( r = rac{a}{b} = rac{2x}{y} \), then:

📌 r - \sqrt{5} r + 5 + \sqrt{5} = 0 \Rightarrow r(-1 - \sqrt{5}) = - (5 + \sqrt{5})

📌 \Rightarrow r = rac{5 + \sqrt{5}}{1 + \sqrt{5}}

📌 r = rac{5 + \sqrt{5}}{1 + \sqrt{5}} \cdot rac{1 - \sqrt{5}}{1 - \sqrt{5}} = rac{(5 + \sqrt{5})(1 - \sqrt{5})}{1 - 5} = rac{5(1 - \sqrt

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