a window is being built and the bottom is a rectangle and the top is a semicircle (picture below). there is 12 meters of framing materials. we want to design the window for maximum area. we can have a window with "a tall rectangle and a small semi-circle" or the opposite "a short wide rectangle with a big semicircle" or anything in between. a student is thinking of different scenarios. he picked three scenarios for r=1 m, r=1.5 m and r=2 m. we know that the height of rectangle will depend on radius of the semicircle given that we have only 12 meters of framing. find the height h under any of theses scenarios.
hint: 2h+2r+πr=12
window framing area optimization
select one:
a. h1=6, h2=3, h3=1.5
b. h1=7.25, h2=2.49, h3=1.2
c. h1=3 h2=4.5, h3=6
d. h1=6.86 h2=4.29, h3=1.72