To classify the triangle with side lengths of 1 cm, 13 cm, and the unknown length (let's call it \( x \) cm), we must first 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. This means:
- \( 1 + 13 > x \) (which simplifies to \( x < 14 \))
- \( 1 + x > 13 \) (which simplifies to \( x > 12 \))
- \( 13 + x > 1 \) (this condition is always satisfied since both \( 13 \) and \( x \) will be positive).
From these inequalities, we can deduce:
- From \( x < 14 \) and \( x > 12 \), the possible value for \( x \) is 13 cm in whole numbers.
Now we can analyze the triangle:
- The sides of the triangle are 1 cm, 13 cm, and 13 cm.
- This means the triangle has two equal sides (the two 13 cm sides), which makes it an isosceles triangle.
Since an isosceles triangle can also potentially be classified as scalene (which it is not in this case) or equilateral (it is not in this case as well), we can say the following:
- The triangle formed is isosceles.
In conclusion, the correct classification for this triangle by its sides is:
- Isosceles