Maximum Area of Triangle With Given Sides

Very Hard Problem Solving Geometry

In a triangle ABC, the length of side AB is 12 cm, and the length of side AC is 16 cm. The angle BAC is the angle between sides AB and AC. Let S be the area of triangle ABC. The area can also be computed using the formula:

$$S = \f\frac{1}{2} \times AB \times AC \times \sin(BAC)$$

What is the maximum possible area of triangle ABC?

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

Hint

Submitted10.9K

Correct10.1K

% Correct93%