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

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

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 x = [-2 ± √(4 + 560)]/2 = [-2 ± √564]/2

📌 √564 = √(4×141) = 2√141 ≈ 2×11.87 = 23.74

📌 x ≈ ( -2 + 23.74 ) / 2 ≈ 21.74 / 2 ≈ 10.87 → not integer.

📌 But let's assume the sum is correct and solve numerically.

📌 Sum: (n−1)² + n² + (n+1)² = n²−2n+1 + n² + n²+2n+1 = 3n² + 2

📌 Set equal to 425:

📌 3n² + 2 = 425 → 3n² = 423 → n² = 141 → n = √141 ≈ 11.874

📌 So smallest integer is n − 1 ≈ 10.874 → not integer — contradiction.

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