Multiple choice

The lengths of two adjacent sides of a rectangle inscribed in a circle are 5 centimeters and 12 centimeters. Quantity A Radius of the circle Quantity B 5.5 centimeters

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
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A Correct answer
Explanation

A rectangle inscribed in a circle has a diagonal equal to the circle's diameter. Using the Pythagorean theorem, the diagonal is sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13. The radius is half the diameter, so r = 13/2 = 6.5. Since 6.5 > 5.5, Quantity A is greater.

AI explanation

A rectangle inscribed in a circle has the diameter of the circle as its diagonal. We find the diagonal using the Pythagorean theorem: the square root of (5 squared plus 12 squared) is the square root of 169, which is 13 cm. The radius is half the diameter, so the radius is 6.5 cm. Quantity A is 6.5 cm and Quantity B is 5.5 cm, making Quantity A greater.

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