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📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 5Question: A hydrologist models groundwater flow through a triangular aquifer section with side lengths of 13 km, 14 km, and 15 km. What is the length of the shortest altitude in kilometers, and how might this relate to the aquifers permeability along the steepest flow path?

📌 Solution: To find the shortest altitude in a triangle with side lengths $ a = 13 $, $ b = 14 $, and $ c = 15 $, we first compute the area using Herons formula. The semi-perimeter $ s $ is:

📌 Thus, the shortest altitude is $ 11.2 $ km, representing the minimal perpendicular distance from the opposite vertex to the steepest flow edge, which may correlate with high-permeability dissipation zones.

📌 Solution: The rectangle with dimensions 5 cm by 12 cm is inscribed in a circle, so its diagonal is the diameter of the circle. Using the Pythagorean theorem:

📌 Thus, the diameter of the circle is 13 cm, and the circumference $ C $ is:

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