To determine the classification of the triangle based on its side lengths, we need to verify if a triangle can be formed with sides measuring 1 cm, 13 cm, and a third side which is a whole number.
Using the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's denote the third side as \( x \). We have:
- \( 1 + 13 > x \) → \( 14 > x \) or \( x < 14 \)
- \( 1 + x > 13 \) → \( x > 12 \)
- \( 13 + x > 1 \) → This inequality is always true since both \( x \) and 13 are positive.
From the inequalities \( x > 12 \) and \( x < 14 \), the only possible value for \( x \) is 13. However, this is already one of the sides of the triangle.
This means that when looking for a third side \( x \), there are no possible lengths that satisfy the triangle inequality while keeping all three sides distinct integers.
Therefore, a triangle with sides of lengths 1 cm, 13 cm, and any integer \( x \) does not exist.
Since a triangle cannot be formed with these lengths, we cannot classify the triangle. If we were to further discuss the type based on the side length alone without formation criteria, if all three sides were indeed lengths that could exist (which they cannot), it would indicate a degenerate case (collinear).
But per your options given, none apply due to the inability to form the triangle with the sides mentioned.
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