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📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 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:

📌 \[ 2 = \frac{a + b - 10}{2} \]

📌 \[ a + b = 14 \]

📌 The area \(A\) of the triangle is given by:

📌 \[ A = \frac{1}{2}ab \]

📌 Using the Pythagorean theorem:

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