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the westin oaks houston at the galleria - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 The radius \(r\) of the inscribed circle is given by:

📌 r = \frac{A}{s} = \frac{54}{18} = 3 \text{ cm}

📌 Thus, the radius of the inscribed circle is \(\boxed{3}\).

📌 A circle is inscribed in a triangle with sides measuring 7 cm, 24 cm, and 25 cm. Calculate the area of the inscribed circle.

📌 First, verify that the triangle is a right triangle using the Pythagorean theorem:

📌 25^2 = 7^2 + 24^2 \quad \Rightarrow \quad 625 = 49 + 576 \quad \Rightarrow \quad 625 = 625

📌 The triangle is confirmed as a right triangle. The area \(A\) of the triangle is:

📌 A = \frac{1}{2} \times 7 \times 24 = 84 \text{ cm}^2

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