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Home » The length is \( 3 \times 12 = 36 \) cm. - RTA

The length is \( 3 \times 12 = 36 \) cm. - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Thus, the length of the longest altitude is $ \boxed{\frac{168}{13}} $ cm.

📌 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?

📌 Solution: The original side length of the equilateral triangle is $ \frac{36}{3} = 12 $ cm. The area of an equilateral triangle is given by:

📌 Original area:

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

📌 New side length: $ 12 + 2 = 14 $ cm. New area:

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

📌 \Delta A = A_2 - A_1 = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3}

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