SOLUTION: determine dimensions of the rectangle of a greatest area that can be inscribed in a semi-circle of radius 15m

Question 814194: determine dimensions of the rectangle of a greatest area that can be inscribed
in a semi-circle of radius 15m
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
the max area rectangle is actually a square.
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s = side of square
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basic geometry leads to a right triangle with:
hypotenuse (h) = r = 15
adjacent side = s/2
opposite side = s
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use pythagorean theorem:
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h = sqrt( s^2 + (s/2)^2 )
h = sqrt( ss + (s/2)(s/2) )
h = sqrt( ss + (ss/4) )
h = sqrt( (4ss/4) + (ss/4) )
h = sqrt( (5ss/4) )
h = sqrt(5)(s/2)
s = 2h/sqrt(5)
s = 30/sqrt(5)
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s = 13.416408 sq.m
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max area = 180 m
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