Multiple choice

Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which of the following pairs can represent (in cm) the possible length and breadth of ABCD?

  1. 24, 10

  2. 24, 12

  3. 25, 9

  4. 25, 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a rectangle inscribed in a circle, the diagonal equals the diameter. Diameter = 2 * 13 = 26 cm. Diagonal^2 = L^2 + B^2 = 26^2 = 676. For option A: 24^2 + 10^2 = 576 + 100 = 676. This works.

AI explanation

Because ABCD is a rectangle inscribed in a circle, its diagonal acts as the diameter of the circle, meaning the diagonal length is 2 times 13, which is 26 cm. Using the Pythagorean theorem for rectangles, the square of the diagonal equals the square of the length plus the square of the breadth. Testing the given pair, 24 squared is 576 and 10 squared is 100, which sum to 676. Since 26 squared is also 676, the possible dimensions are 24 cm and 10 cm.

Keep practicing — related questions