What's the largest possible rectangle inside of the 3-4-5 right triangle?

We will determine the largest possible rectangle that can fit inside a 3-4-5 right triangle. Using algebra and optimization techniques (quadratic equation and the vertex of a parabola), we explore how the rectangle’s dimensions relate to the triangle's proportions. Perfect for algebra and precalculus students to have a first-hand experience of the optimization problems.
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#math #algebra #mathbasics