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Home » ‘Plague Tale’ Revealed: The Chilling Rituals and Fears That Swept a Nation - Dachbleche24

‘Plague Tale’ Revealed: The Chilling Rituals and Fears That Swept a Nation - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 To find the shortest altitude, we first compute the area of the triangle using Heron’s formula, then divide by the longest side (since the altitude to the longest side is the shortest).

📌 Let the sides be \(a = 13\), \(b = 14\), \(c = 15\). Compute the semi-perimeter \(s\):

📌 s = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21

📌 Apply Heron’s formula:

📌 A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \times 8 \times 7 \times 6}

📌 = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{7056}

📌 The altitudes \(h_a\), \(h_b\), \(h_c\) corresponding to sides \(a\), \(b\), \(c\) are given by:

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Solution: The perimeter of the original triangle is:
P = 9 + 12 + 15 = 36 \text{ cm}
So, each side of the new equilateral triangle is:
s = \frac{36}{3} = 12 \text{ cm}
The area of the original triangle (a right triangle) is:
A_{\text{original}} = \frac{1}{2} \cdot 9 \cdot 12 = 54 \text{ cm}^2
The area of the equilateral triangle is:
A_{\text{new}} = \frac{\sqrt{3}}{4} \cdot 12^2 = \frac{\sqrt{3}}{4} \c...
The increase in area is:
\Delta A = 36\sqrt{3} - 54

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