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Home » So only guaranteed prime factor is 3. And we have at least $3^1$. - Baxtercollege

So only guaranteed prime factor is 3. And we have at least $3^1$. - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 s' = 12 - 4 = 8 \text{ cm}

📌 A' = \frac{\sqrt{3}}{4} (8)^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3}

📌 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.**Question:** A soil scientist is analyzing a plot of land shaped like a right triangle. The hypotenuse of the triangle is \(10\) meters, and the radius of the inscribed circle is \(2\) meters. Determine the ratio of the area of the inscribed circle to the area of the triangle.

📌 Let the legs of the right triangle be \(a\) and \(b\), and the hypotenuse \(c = 10\). The radius \(r\) of the inscribed circle is given by:

📌 Given that \(r = 2\), we have:

📌 \[ 2 = \frac{a + b - 10}{2} \]

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