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homewood suites by hilton arlington rosslyn key bridge - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 d = \sqrt{x^2 + x^2 + x^2} = \sqrt{3x^2} = x\sqrt{3}

📌 \boxed{x\sqrt{3}}

📌 Question: A marine safety consultant studies a triangular coral reef formation with sides of 10 m, 10 m, and 12 m. What is the radius of the inscribed circle in meters?

📌 Let $ a = 10 $, $ b = 10 $, and $ c = 12 $. The semi-perimeter is:

📌 s = \frac{10 + 10 + 12}{2} = 16

📌 Using Heron’s formula for the area:

📌 A = \sqrt{16(16 - 10)(16 - 10)(16 - 12)} = \sqrt{16(6)(6)(4)} = \sqrt{2304} = 48

📌 The radius $ r $ of the inscribed circle is:

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