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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:

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