To classify the triangle by its sides, we need to determine if the triangle can exist with the given side lengths of 1 cm and 13 cm, and what the third side must be.
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. Let’s denote the third side as \( x \). We know:
- \( 1 + 13 > x \) → \( x < 14 \)
- \( 1 + x > 13 \) → \( x > 12 \)
- \( 13 + x > 1 \) → This condition will always hold since \( x \) is a positive whole number.
From the inequalities \( x < 14 \) and \( x > 12 \), we find that \( x \) can only be 13.
Thus, the side lengths of the triangle are 1 cm, 13 cm, and 13 cm.
Since two sides are equal (13 cm and 13 cm), the triangle is classified as:
Isosceles
So the answer is:
O isosceles
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