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Home » Question: An equilateral triangle has an area of $25\sqrt3\,\textcm^2$. If each side is increased by $4\,\textcm$, by how many square centimeters does the area increase? - AMAZONAWS

Question: An equilateral triangle has an area of $25\sqrt3\,\textcm^2$. If each side is increased by $4\,\textcm$, by how many square centimeters does the area increase? - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
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?

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📌 \[ n = \frac{\log(1.8)}{\log(1.02)} \approx 29.25 \]
📌 s' = 12 - 2 = 10 \, \text{cm}
📌 Thus, \(x = 7\).
📌 Solution: This is a surjective function problem: count the number of ways to partition 7 distinct species into 4 non-empty habitats. Using the inclusion-exclusion principle: $ \sum_{k=0}^4 (-1)^k \binom{4}{k} (4 - k)^7 $. Calculating: $4^7 - \binom{4}{1}3^7 + \binom{4}{2}2^7 - \binom{4}{3}1^7$. Compute each term: $16384 - 4 \times 2187 + 6 \times 128 - 4 \times 1 = 16384 - 8748 + 768 - 4 = 8400$. The final answer is $\boxed{8400}$.**Question:
📌 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?

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  • So, \( 36 + b^2 = 100 \).
  • \( x + y = 13 \)
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