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Rectangle in a circle (Posted on 2017-11-07) Difficulty: 2 of 5
What is the maximum perimeter
of a rectangle inscribed in
a half of a circle with radius R?

No Solution Yet Submitted by Ady TZIDON    
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Solution Another calculus solution | Comment 2 of 3 |
Let the height of the rectangle be h.
Then the perimeter = 2h+4sqrt(R^2-h^2).

The derivative with respect to h = 2 - 4h/sqrt(R^2-h^2).
Set this equal to 0 and solve for h,
  yielding h = R/sqrt(5)
  
Then the perimeter =   
  2R/sqrt(5) + 4sqrt(4R^2/5) = 10R/sqrt(5) = 2R*sqrt(5)

  Posted by Steve Herman on 2017-11-07 12:19:28
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