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Home » Length: \( 3w = 24 \). - Red Crowns

Length: \( 3w = 24 \). - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 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

📌 Thus, the area increases by \(\boxed{13\sqrt{3}}\) square centimeters.

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