A landscape architect is designing a water feature in the shape of a semicircle with a radius of 4 m 4\text{ m} . A rectangular pathway is to be constructed with its base along the diameter of the semicircle, and its other two vertices touching the semicircle. Determine the dimensions of the path that maximize its area, where l l is length and w w is width.

l = 4 2 m l=4\sqrt2\text{ m} w = 2 2 m w=2\sqrt2\text{ m}

l = 4 2 m l=4\sqrt2\text{ m} w = 2 m w=\sqrt2\text{ m}

l = 4 2 m l=4\sqrt2\text{ m} w = 4 2 m w=4\sqrt2\text{ m}

l = 2 2 m l=2\sqrt2\text{ m} w = 2 2 m w=2\sqrt2\text{ m}

A landscape architect is designing a water feature...

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