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📅 May 4, 2026 👤 scraface

May 04, 2026

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In a right triangle with legs of lengths 9 cm and 12 cm, find the radi...
First, we find the hypotenuse \(c\) of the right triangle using the Py...
c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \text{ cm}
The area \(A\) of the triangle is:
A = \frac{1}{2} \times 9 \times 12 = 54 \text{ cm}^2
The semi-perimeter \(s\) of the triangle is:
s = \frac{9 + 12 + 15}{2} = 18 \text{ cm}
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 \(\boxed{3}\).

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