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Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a?
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.
What else can I help you with?
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming?
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming
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