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Home » Average speed is \( \frac5005.5 \approx 90.91 \) km/h. - Baxtercollege

Average speed is \( \frac5005.5 \approx 90.91 \) km/h. - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Question: An equilateral triangle has an area of $25\sqrt{3}\,\text{cm}^2$. If each side is increased by $4\,\text{cm}$, by how many square centimeters does the area increase?

📌 Solution: The area of an equilateral triangle is $\frac{\sqrt{3}}{4} s^2$. Solving for original side $s$: $\frac{\sqrt{3}}{4} s^2 = 25\sqrt{3} \Rightarrow s^2 = 100 \Rightarrow s = 10\,\text{cm}$. New side: $14\,\text{cm}$. New area: $\frac{\sqrt{3}}{4} \cdot 14^2 = 49\sqrt{3}$. Increase: $49\sqrt{3} - 25\sqrt{3} = 24\sqrt{3}$. Thus, $\boxed{24\sqrt{3}}$.

📌 Question: A historical astrolabe features a right triangle

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