Question

A square is inscribed in a ˚le. If the ˚le has an area of 9π, what is the length of the square's diagonal?

a) 3√2
b) 6
c) 3
d) 2√3

Answer 1

The diagonal of the square inscribed in a circle with an area of 9π is 6.

Step-by-step explanation:

The student has asked a geometry question about the relationship between the area of a circle and the diagonal of a square inscribed within it. Given that the area of the circle is 9π, we must first find the radius of the circle. Since the area A of a circle is given by A = πr², solving for r gives us r = 3.

Because the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square. Therefore, the diagonal d of the square is 2r, which is 2(3) = 6. This means the correct answer is b) 6.