Question: The figures show a rectangle, a circle, and a semicircle inscribed in a triangle bounded by the coordinate axes and the first-quadrant portion of the

The figures show a rectangle, a circle, and a semicircle inscribed in a triangle bounded by the coordinate axes and the first-quadrant portion of the line with intercepts (3, 0) and (0, 4). Find the dimensions of each inscribed figure such that its area is maximum. State whether calculus was helpful in finding the required dimensions. Explain your reasoning.

4 3 2 1 2 1 2 3 4 4 3 2

4 3 2 1 2 1 2 3 4 4 3 2 1 y 1 2 3 4 X 4- 32 y 1 1234 X

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