Determine Length of Side AB in Triangle ABC

Very Hard Problem Solving Geometry

Consider triangle ABC, where angle A measures 60 degrees and the length of side BC is 12 units.

Statement (1): The length of side AB is equal to the length of side AC.

Statement (2): The area of triangle ABC is 36 square units.

What is the length of side AB?

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.

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