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Home » Solution:** First, approximate the interval endpoints using \( \pi \approx 3.14 \): - 500apps

Solution:** First, approximate the interval endpoints using \( \pi \approx 3.14 \): - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 An equilateral triangle has an area of \( 36\sqrt{3} \) square centimeters. If each side of the triangle is increased by 2 cm, by how many square centimeters does the area increase?

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\frac{\sqrt{3}}{4} s^2 = 36\sqrt{3} \implies \frac{s^2}{4} = 36 \impli...
New side length after decreasing by 4 cm:
s' = 12 - 4 = 8 \text{ cm}
A' = \frac{\sqrt{3}}{4} (8)^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt...
Reduction in area:
\Delta A = 36\sqrt{3} - 16\sqrt{3} = 20\sqrt{3}
Thus, the area is reduced by \(\boxed{20\sqrt{3}}\) square centimeters...
Let the legs of the right triangle be \(a\) and \(b\), and the hypoten...
Given that \(r = 2\), we have:
\[ 2 = \frac{a + b - 10}{2} \]

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