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Home » Somme des multiples de 15 (pour éviter le double comptage) : \(15 + 30 + \ldots + 90\). - AMAZONAWS

Somme des multiples de 15 (pour éviter le double comptage) : \(15 + 30 + \ldots + 90\). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 36\sqrt{3} - 16\sqrt{3} = 20\sqrt{3}

📌 Thus, the area decreases by $ \boxed{20\sqrt{3}} $.

📌 Question: A triangle has side lengths 13 cm, 14 cm, and 15 cm. Find the length of the shortest altitude in centimeters.

📌 Use Heron’s formula to compute the area. Semi-perimeter $ s $:

📌 Area $ A $:

📌 = \sqrt{21 \cdot 8 \cdot 42} = \sqrt{7056} = 84 \text{ cm}^2

📌 The shortest altitude corresponds to the longest side, which is 15 cm. Using area formula $ A = \frac{1}{2} \times \text{base} \times \text{height} $:

📌 = \frac{1}{2} \cdot 15 \cdot h \Rightarrow 168 = 15h \Rightarrow h = \frac{168}{15} = 11.2

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