A Constrained Right Triangle

★ 6/10plane geometry Extrema inequality Triangle Geometry

Problem

The sides $a, b, c$ of a right triangle satisfy

3 \leqslant a \leqslant 5 \leqslant b \leqslant 8 \leqslant c \leqslant 9.

Find the maximum possible area of the triangle.

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Extrema, inequality, Triangle Geometry

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