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Home » = 7 \times 13 - Esdistancia

= 7 \times 13 - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 h_a = \frac{2A}{a}, \quad h_b = \frac{2A}{b}, \quad h_c = \frac{2A}{c}

📌 The shortest altitude corresponds to the longest side, which is \(c = 15\):

📌 h_{\text{min}} = \frac{2 \times 84}{15} = \frac{168}{15} = \frac{56}{5} = 11.2

📌 Thus, the length of the shortest altitude is \(\boxed{\frac{56}{5}}\) units.

📌 An equilateral triangle has an area of \(36\sqrt{3}\) square centimeters. If each side of the triangle is decreased by 4 cm, by how many square centimeters is the area reduced?

📌 The area \(A\) of an equilateral triangle with side \(s\) is:

📌 Given \(A = 36\sqrt{3}\), solve for \(s\):

📌 \frac{\sqrt{3}}{4} s^2 = 36\sqrt{3} \implies \frac{s^2}{4} = 36 \implies s^2 = 144 \implies s = 12 \text{ cm}

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