Your relatives are wanting to build a log-cabin-style vacation home, and they ask for your technical advice during its design. they want to make the strongest ridge beams possible from white oak. the supplier they found is able to cut rectangular cross sections from 12-ft-long, 18-in-diameter logs. a) determine the base and height dimensions of the optimum cross section. (hint: "strongest rectangular cross section" = maximum section modulus. start by writing the base and height of a rectangle inscribed in a circle as a function of a single variable, θ, and then find the maximum of that function.) b) using the cross-section from part (a) and knowing the ultimate strength of white oak in compression is 7.4 ksi, what is the maximum allowable uniform distributed load intensity w (kips/ft) that this beam would support with simple supports 12 feet apart (l = 12 ft)?