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Home » You’ll Cry, Scream, and Want More—The Cult-Approved Dragon and Dungeons Movie You Needed! - inBeat

You’ll Cry, Scream, and Want More—The Cult-Approved Dragon and Dungeons Movie You Needed! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: Find the length of the longest altitude of a triangle with side lengths $ 7 $ cm, $ 10 $ cm, and $ 13 $ cm.

📌 Solution: First, compute the area using Heronâs formula. Let $ a = 7 $, $ b = 10 $, $ c = 13 $. The semi-perimeter $ s $ is:

📌 s = rac{7 + 10 + 13}{2} = 15

📌 The area $ A $ is:

📌 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}

📌 \sqrt{1200} = \sqrt{100 \cdot 12} = 10\sqrt{12} = 10 \cdot 2\sqrt{3} = 20\sqrt{3} ext{ cm}^2

📌 The altitude $ h $ corresponding to a side $ b $ is given by:

📌 A = rac{1}{2} b h \Rightarrow h = rac{2A}{b}

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