Multiple choice

The maximum area of a rectangle inscribed in a circle of radius $5$ cm is

  1. $25$ sq. cm
  2. $50$ sq. cm
  3. $100$ sq.cm
  4. $\displaystyle \frac{25}{2}$ sq.cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A rectangle inscribed in a circle has maximum area when it is a square. Diagonal of square = diameter of circle = 10 cm. Side s = 10 / sqrt(2). Area = s^2 = 100 / 2 = 50 sq cm.

AI explanation

The maximum area of a rectangle inscribed in a circle occurs when the rectangle is a square, which has its diagonals equal to the diameter of the circle. The diameter of the circle is 2 * 5 = 10 cm. If the side of the square is s, then by the Pythagorean theorem, s^2 + s^2 = 10^2, meaning 2*s^2 = 100 and s^2 = 50. The area of the square is s^2, which equals 50 sq. cm.

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