To determine the classification of the triangle based on its side lengths, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.
Given side lengths are 1 cm and 13 cm. We will let \( x \) be the length of the third side, which is a whole number.
Using the triangle inequality:
- \( 1 + 13 > x \) which simplifies to \( 14 > x \) or \( x < 14 \).
- \( 1 + x > 13 \) which simplifies to \( x > 12 \).
- \( 13 + x > 1 \) which is always true since \( x \) is a positive whole number.
From the inequalities \( x < 14 \) and \( x > 12 \), we find that \( x \) can only be 13 (as it is the only whole number that meets both conditions). However, this would mean that we have two sides of the same length (1 cm and 13 cm, and another 13 cm), which describes an isosceles triangle.
Conclusion: The triangle is classified as isosceles.
Thus, the correct response is: isosceles.
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