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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:
This circumference defines the full loop the drone follows, optimizing coverage over the rectangular zone.
Question: A historian analyzing ancient geometric instruments discovers a triangular tablet with integer side lengths forming a right triangle, where the hypotenuse is $ z $ and the inradius is $ c $. If $ z = 25 $ and $ c = 5 $, what is the ratio of the area of the inscribed circle to the area of the triangle?
Solution: For a right triangle with legs $ a $, $ b $, hypotenuse $ z = 25 $, and inradius $ c = 5 $, we use the formula for the inradius of a right triangle:
Substitute $ c = 5 $ and $ z = 25 $:
We also have $ a + b = 35 $. Square both sides:
This ratio indirectly supports ergonomic design in ancient measuring devices, where geometric harmony maximized precision.
Solution: The area $ A $ of an equilateral triangle with side $ s $ is:
