Area of Right Triangle Based on Side Lengths

Hard Problem Solving Geometry

In triangle PQR, the lengths of the sides PQ, PR, and QR are represented as $a$, $b$, and $c$, respectively. The triangle is known to be a right triangle where the right angle is at point P.

What is the area of triangle PQR?

Statement (1): The length of side PQ is 6 units.

Statement (2): The length of side QR is 8 units.

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

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