Question

In \( \Delta ABC \), \( A, B, C \) are in arithmetic progression and \( a : c = 1 : 2 \). If \( b = 4\sqrt{3} \) cm, then the area of \( \Delta ABC \) (in sq. cm) is:

• A. \( 16\sqrt{3} \)
• B. \( 12\sqrt{3} \)
• C. \( 8\sqrt{3} \)
• D. \( 6\sqrt{3} \)

Hint:

For triangles with sides in arithmetic progression, use Heron’s formula and the relationships between the sides to find the area.

Answer 1

The Correct Option is C

Given that \( A, B, C \) are in arithmetic progression, and \( a : c = 1 : 2 \), we can use Heron's formula to find the area of the triangle. By substituting the given values and solving the equation, we find the area of \( \Delta ABC \) to be \( 8\sqrt{3} \) square centimeters.