Multiple choice

A rectangle with one side equal to 6 cm is inscribed in a circle of radius 5 cm. Then what is the area of the rectangle?

  1. $36cm^2$
  2. $42cm^2$
  3. $48cm^2$
  4. $54cm^2$
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C Correct answer
Explanation

A rectangle inscribed in a circle has its diagonal equal to the diameter of the circle. Given radius 5, diameter = 10. Using the Pythagorean theorem with one side 6, the other side is sqrt(10^2 - 6^2) = 8. Area = 6 * 8 = 48.

AI explanation

The diameter of the circle is the diagonal of the inscribed rectangle, measuring 2 * 5 = 10 cm. Using the Pythagorean theorem, the other side of the rectangle is sqrt(10^2 - 6^2) = 8 cm. The area of the rectangle is length multiplied by breadth, which is 8 * 6 = 48 square centimeters.

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