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Home » \( S_15 = \frac152(10 + 42) \) - Richter Guitar

\( S_15 = \frac152(10 + 42) \) - Richter Guitar

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \boxed{16.25\pi}

📌 Question: An archaeologist discovers a triangular stone slab with side lengths 13 cm, 14 cm, and 15 cm. What is the radius of the inscribed circle?

📌 Solution: To find the radius $r$ of the inscribed circle of a triangle with sides $a = 13$, $b = 14$, and $c = 15$, we use the formula:

📌 r = \frac{A}{s}

📌 where $A$ is the area of the triangle and $s$ is the semi-perimeter:

📌 s = \frac{a + b + c}{2} = \frac{13 + 14 + 15}{2} = 21

📌 Using Heron’s formula for area:

📌 r = \frac{84}{21} = 4

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