Multiple choice

In a town's central park, a beautiful fountain is constructed in the shape of a circular basin, which is inscribed in a square platform. Within this circular basin, a skilled artist creates a captivating artwork of a triangular shape with sides 5 m, 12 m and 13 m such that all three endpoints of the triangular artwork touch the boundary of the circular basin. What is the area of the square platform?

  1. 42.25 m2

  2. 100 m2

  3. 156.25 m2

  4. 169 m2

  5. a
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D Correct answer
Explanation

A triangle with sides 5, 12, 13 is a right-angled triangle. The circumradius of a right triangle is half the hypotenuse, so the radius of the circle is 13/2 = 6.5 m. The circle is inscribed in a square, so the side of the square is equal to the diameter of the circle, which is 13 m. Area of the square = 13*13 = 169 m^2.

AI explanation

The triangle formed by the artwork has sides of 5 m, 12 m, and 13 m, meaning it is a right-angled triangle. The hypotenuse of this right triangle acts as the diameter of the circular basin, making the diameter 13 m. The square platform encloses this circle, so the side length of the square equals the diameter of the circle, which is 13 m. The area of the square platform is 13 squared, which equals 169 m2.

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