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how long does walking pneumonia last - Belip

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Question: A triangle has side lengths of $ 7 \, \text{cm} $, $ 10 \, \text{cm} $, and $ 13 \, \text{cm} $. What is the area of the triangle?

📌 Solution: Use Heron’s formula. The semi-perimeter is:

📌 s = \frac{7 + 10 + 13}{2} = 15 \, \text{cm}.

📌 A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{15(15 - 7)(15 - 10)(15 - 13)} = \sqrt{15 \cdot 8 \cdot 5 \cdot 2} = \sqrt{1200} = 10\sqrt{12} = 20\sqrt{3} \, \text{cm}^2.

📌 \boxed{20\sqrt{3}}

📌 Question: A right circular cone has a base radius of $ 5x $ and a slant height of $ 13x $. What is the total surface area of the cone in terms of $ x $?

📌 Solution: The total surface area of a cone is the sum of the base area and the lateral surface area. The base area is:

📌 \pi (5x)^2 = 25\pi x^2.

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