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Home » So \(n = 20\) (since \(n > 0\)). - Belip

So \(n = 20\) (since \(n > 0\)). - Belip

📅 May 7, 2026 👤 scraface

May 07, 2026

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📌 Thus, the volume increases by a factor of \(\boxed{27}\).

📌 Question:** In a right triangle, one leg is 6 cm and the hypotenuse is 10 cm. Find the length of the shortest altitude.

📌 Let the triangle have legs \(a = 6\) cm, hypotenuse \(c = 10\) cm. Use the Pythagorean theorem to find the other leg \(b\):

📌 b = \sqrt{c^2 - a^2} = \sqrt{100 - 36} = \sqrt{64} = 8 \text{ cm}

📌 Area of the triangle:

📌 A = \frac{1}{2} \cdot 6 \cdot 8 = 24 \text{ cm}^2

📌 The altitudes corresponding to each side are found using \(A = \frac{1}{2} \times \text{base} \times \text{height}\).

📌 Altitude to leg \(a = 6\):

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