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gurvinder singh sandhu Grade: 12
        

show that all the rectangles of maximum perimeter which can be inscribed in a circle of radius 'a' is square of side root2a

6 years ago

Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear girvinder,


The largest rectangle would be a square. If the circle has radius a, the diameter is 2a. This diameter would also be the diameter of a square of side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2.
2b2 = 4a2
b2 = 2a2
b = √(2a2) or a√2 = the length of the sides of the square
The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.


 











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Sagar Singh


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6 years ago
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