To determine the classification of the triangle based on its side lengths, we first need to ensure that it satisfies the triangle inequality theorem:
For any triangle with sides of lengths \( a \), \( b \), and \( c \), the following conditions must hold:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
In your case, we have two sides measured as 1 cm and 13 cm. Let's denote the third side as \( x \).
Now, we will apply the triangle inequality conditions:
-
\( 1 + 13 > x \)
\( 14 > x \) Thus, \( x < 14 \). -
\( 1 + x > 13 \)
\( x > 12 \). -
\( 13 + x > 1 \)
This condition is always satisfied for positive \( x \).
From the inequalities \( x < 14 \) and \( x > 12 \), we find that the only possible integer value for \( x \) is \( 13 \).
Thus, the side lengths of the triangle are 1 cm, 13 cm, and 13 cm.
Now let's classify the triangle by its sides:
- It has two sides of equal length (13 cm), making it an isosceles triangle.
Therefore, the answer is isosceles.