To determine how many triangles can be formed with segments measuring 34 cm, 13 cm, and 38 cm, we need to apply the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's denote the segments as:
- \( a = 34 \) cm
- \( b = 13 \) cm
- \( c = 38 \) cm
We need to check the following inequalities:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
Now we calculate each inequality:
-
Checking \( a + b > c \): \( 34 + 13 > 38 \)
\( 47 > 38 \) (True) -
Checking \( a + c > b \): \( 34 + 38 > 13 \)
\( 72 > 13 \) (True) -
Checking \( b + c > a \): \( 13 + 38 > 34 \)
\( 51 > 34 \) (True)
Since all three conditions of the triangle inequality are satisfied, we can conclude that:
1 triangle can be formed from these segments.