Solution, using the Arithmetic Mean -- Geometric Mean Inequality
Now, this area is attained only when r = 50 - r (by the AM-GM ineq.)
and so, r = 25. Therefore ø = 2.
Interpret.
Draw a sketch of the sector with maximum area. It has a central angle larger
than a quarter circle but less than a semicircle.
Use a spreadsheet to make a table and graph of the area as ø increases
with a fixed perimeter (like P = 100).
What if you chose to work with the area equation in terms of ø?
Will the use of the AM -- GM ineq. be possible? Try it.
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