To determine the classification of the triangle by its sides, we'll first note the lengths of the two given sides: 1 cm and 13 cm.
A triangle's side lengths must satisfy 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 \( x \) (where \( x \) is a whole number).
We have the following conditions based on the triangle inequality theorem:
- \( 1 + 13 > x \) (which simplifies to \( 14 > x \) or \( x < 14 \))
- \( 1 + x > 13 \) (which simplifies to \( x > 12 \))
- \( 13 + x > 1 \) (since \( 13 > 1 \), this condition is always satisfied for positive \( x \))
From the inequalities:
- From condition 1: \( x < 14 \)
- From condition 2: \( x > 12 \)
Thus, the only whole number value that meets both conditions is \( x = 13 \).
Now we can summarize the side lengths:
- The sides of the triangle are 1 cm, 13 cm, and 13 cm.
Classification by sides:
- An isosceles triangle has at least two sides that are equal in length. Here, we have two sides that are both 13 cm.
- It is not equilateral because not all three sides are equal (the sides are 1 cm, 13 cm, and 13 cm).
- It is not scalene because scalene triangles have all sides of different lengths (which is not the case here).
Thus, the triangle is classified as isosceles.
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