Hypotenuse Length in Right Triangle

Very Hard Problem Solving Geometry

In triangle ABC, angle A is a right angle. The lengths of the legs AB and AC are in the ratio 3:4. Let the length of AB be represented as $3x$ and the length of AC be represented as $4x$ for some positive value of $x$.

What is the length of the hypotenuse BC?

Statement (1): The perimeter of triangle ABC is 30.

Statement (2): The area of triangle ABC is 48.

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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