To determine the classification of the triangle by its sides, we need to examine the side lengths provided along with the triangle inequality theorem.
The side lengths given are 1 cm and 13 cm. Let's denote the third side as \( x \) (where \( x \) is a whole number).
According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, we need to satisfy the following inequalities:
- \( 1 + 13 > x \) → \( 14 > x \) → \( x < 14 \)
- \( 1 + x > 13 \) → \( x > 12 \)
- \( 13 + x > 1 \) → This inequality is always true since \( x \) is a positive number.
From these inequalities, we can determine that the value of \( x \) must satisfy:
- \( 12 < x < 14 \)
Since \( x \) must be a whole number, the only possible value for \( x \) is 13.
Now, we have the three sides of the triangle: 1 cm, 13 cm, and 13 cm.
Since this triangle has two sides of equal length (13 cm), it is classified as an isosceles triangle.
The classification by its sides is: isosceles.
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