To classify the triangle by its sides, we must confirm that the given side lengths can indeed form a valid triangle. The side lengths given are 1 cm and 13 cm. Let's denote the third side as \( x \).
For a valid triangle, the triangle inequality must hold true, which states:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
For the side lengths \( a = 1 \) cm, \( b = 13 \) cm, and \( c = x \):
- \( 1 + 13 > x \) → \( 14 > x \) (which means \( x < 14 \))
- \( 1 + x > 13 \) → \( x > 12 \)
- \( 13 + x > 1 \) (this condition will always be true since \( x > 0 \))
From these inequalities, we can combine the first two conditions:
- From \( x < 14 \) and \( x > 12 \), we see that the only integer value satisfying this is \( x = 13 \).
Thus, the side lengths are 1 cm, 13 cm, and 13 cm.
Now, to classify the triangle:
- Since two sides are equal (13 cm and 13 cm), it is an isosceles triangle.
So the answer is isosceles.