Explanation:

Let’s break down the problem:

- The radius (r) of the inscribed circle in an equilateral triangle of side a = 24 cm is:

r = a / (2v3) = 24 / (2v3) = 12/v3 = 4v3 cm

- The diameter of the circle is 2r = 8v3 cm.

- The largest square inscribed in a circle has its diagonal equal to the circle's diameter.

So, diagonal of square = 8v3 cm

- Side of square, s = (diagonal)/v2 = (8v3)/v2 = 8v(3/2) = 8 × v1.5 ˜ 8 × 1.225 = 9.798 cm (but let's keep it exact)

- Area of square = s² = [8v(3/2)]² = 64 × 3/2 = 96 cm²

Option 4: 96 is correct.

- Option 1 (48), Option 2 (72), and Option 3 (54) do not match the calculated value.

- Correct method is to inscribe the square in the circle, not directly in the triangle.

- The correct answer is Option 4: 96 .