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Home » Subtract (iv) from (v): - American Beagle Club

Subtract (iv) from (v): - American Beagle Club

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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

📌 \[ A = \pi r^2 = \pi (5)^2 = 25\pi \text{ square meters} \]

📌 Hence, the area of the circular garden is \(\boxed{25\pi}\) square meters.

📌 Question:** A mammalogist studying the Arctic tundra uses a triangular net to trap tracks of mammals for observation. The net is in the shape of a right triangle with legs measuring 5 meters and 12 meters. What is the radius of the circle that can be inscribed within this triangle?

📌 For a right triangle, the radius \( r \) of the inscribed circle can be calculated using the formula:

📌 \[ r = \frac{a + b - c}{2} \]

📌 where \( a \) and \( b \) are the legs and \( c \) is the hypotenuse. First, compute the hypotenuse \( c \):

📌 \[ c = \sqrt{a^2 + b^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ meters} \]

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