A tunnel section is designed to have the shape of a rectangle surmounted by a semicircular
roof. The total cross-sectional area A of the tunnel is fixed, but the perimeter
must be minimised to save building costs. Find the optimal dimensions of the tunnel.

Question

A tunnel section is designed to have the shape of a rectangle surmounted by a semicircular
roof. The total cross-sectional area A of the tunnel is fixed, but the perimeter
must be minimised to save building costs. Find the optimal dimensions of the tunnel.

z4k4r1y4 · Answer

I got as far as:
$$x=\sqrt{2A/(1+\pi/4)}$$

z4k4r1y4 · Answer

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