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Home » \(A\) = configurations without I, - Aurero

\(A\) = configurations without I, - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 rac{1}{4}s^2 = 25 \Rightarrow s^2 = 100 \Rightarrow s = 10 ext{ cm}

📌 The new side length is $ s + 4 = 14 $ cm. Compute the new area:

📌 A_{ ext{new}} = rac{\sqrt{3}}{4}(14)^2 = rac{\sqrt{3}}{4} \cdot 196 = 49\sqrt{3} ext{ cm}^2

📌 \Delta A = 49\sqrt{3} - 25\sqrt{3} = 24\sqrt{3} ext{ cm}^2

📌 Thus, the area increases by $ oxed{24\sqrt{3}} $ cmÂ².

📌 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

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