Area of Right Triangle Sufficiency

Very Hard Data Sufficiency Determining Sufficiency

Given a right triangle with legs of length $a$ and $b$ and a hypotenuse of length $c$, we want to determine if the area of the triangle is greater than 20 square units.

Statement (1): The lengths of the legs satisfy $a + b > 10$.

Statement (2): The length of the hypotenuse $c$ is greater than 5 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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