SOLUTION: Determine the area of the largest rectangle that can be inscibed in the circle x^2 + y^2=a^2

Question 749111: Determine the area of the largest rectangle that can be inscibed in the circle x^2 + y^2=a^2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine the area of the largest rectangle that can be inscibed in the circle x^2 + y^2=a^2
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By "largest" I assume you mean "has the greatest area".
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That rectangle would be a square.
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If the square fits inside, it's diagonal must be the
diameter of the circle.
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The diameter = 2*radius = 2*a
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Letting the sides be "x" you get:
x^2 + x^2 = (2a)^2
2x ^2 = 4a^2
x = a*sqrt(2)
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So the area is x*x = (a*sqrt(2))^2 = 2a^2 sq. units
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Cheers,
Stan H.
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