Multiple choice

A rectangle with one side equal to $4$ cm is inscribed in a circle of diameter $5$ cm. Then the area of the rectangle is

  1. $12 cm^2$
  2. $15 cm^2$
  3. $16 cm^2$
  4. $8\sqrt{2} cm^2 $
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A Correct answer
Explanation

Rectangle inscribed in a circle: diagonal = diameter = 5. One side = 4. By Pythagorean theorem, other side = sqrt(5^2 - 4^2) = sqrt(25 - 16) = sqrt(9) = 3. Area = 4 * 3 = 12.

AI explanation

The diameter of the circle is the diagonal of the inscribed rectangle, measuring 5 cm. Using the Pythagorean theorem, the other side of the rectangle is the square root of 5 squared minus 4 squared, which is 3 cm. The area of the rectangle is length multiplied by width, giving 4 cm times 3 cm. The area is 12 cm squared.

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