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Home » We seek integer solutions $(x, y)$. Rearranging: - Carbonext

We seek integer solutions $(x, y)$. Rearranging: - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question:** An equilateral triangle has a perimeter of 36 cm. If each side is increased by 2 cm, by how many square centimeters does the area increase?

📌 An equilateral triangle with perimeter 36 cm has side length:

📌 Initial area:

📌 A_1 = \frac{\sqrt{3}}{4} \cdot 12^2 = \frac{\sqrt{3}}{4} \cdot 144 = 36\sqrt{3} \text{ cm}^2

📌 New side length is \(12 + 2 = 14\) cm, so the new area \(A_2\) is:

📌 A_2 = \frac{\sqrt{3}}{4} \cdot 14^2 = \frac{\sqrt{3}}{4} \cdot 196 = 49\sqrt{3} \text{ cm}^2

📌 Increase in area:

📌 \Delta A = A_2 - A_1 = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3} \text{ cm}^2

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