Triangle Side Lengths Sufficiency

Hard Data Sufficiency Determining Sufficiency

In a certain triangular park, the sides are represented by the lengths $a$, $b$, and $c$, where $a$, $b$, and $c$ are the lengths of the sides of the triangle in meters. Is it possible to form a triangle with these sides?

Statement (1): $a + b = 15$ and $c = 10$.

Statement (2): $a = 8$, $b = 6$, and $c = 5$.

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 together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Hint

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