Jeff is building triangles with different lengths of cm rods. He has two rods measuring 6cm and 9cm. Which of the following would not form a triangle if laid them end to end? 3cm,5cm,6cm or 9cm?
3cm. 6cm+3cm just equal the third side, 9cm, making aline, not a triangle.
To determine which of the given rods would not form a triangle when laid end to end, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each option:
1. 3cm, 5cm, 6cm:
- The sum of the lengths of 3cm and 5cm is 8cm, which is greater than 6cm.
- The sum of the lengths of 5cm and 6cm is 11cm, which is greater than 3cm.
- The sum of the lengths of 3cm and 6cm is 9cm, which is greater than 5cm.
Therefore, the lengths 3cm, 5cm, and 6cm can form a triangle.
2. 3cm, 5cm, 9cm:
- The sum of the lengths of 3cm and 5cm is 8cm, which is less than 9cm.
- The sum of the lengths of 5cm and 9cm is 14cm, which is greater than 3cm.
- The sum of the lengths of 3cm and 9cm is 12cm, which is greater than 5cm.
Therefore, the lengths 3cm, 5cm, and 9cm can form a triangle.
3. 3cm, 6cm, 9cm:
- The sum of the lengths of 3cm and 6cm is 9cm, which is equal to 9cm (not greater).
- The sum of the lengths of 6cm and 9cm is 15cm, which is greater than 3cm.
- The sum of the lengths of 3cm and 9cm is 12cm, which is greater than 6cm.
Therefore, the lengths 3cm, 6cm, and 9cm can form a triangle.
4. 5cm, 6cm, 9cm:
- The sum of the lengths of 5cm and 6cm is 11cm, which is greater than 9cm.
- The sum of the lengths of 6cm and 9cm is 15cm, which is greater than 5cm.
- The sum of the lengths of 5cm and 9cm is 14cm, which is greater than 6cm.
Therefore, the lengths 5cm, 6cm, and 9cm can form a triangle.
In conclusion, the rod measuring 3cm would not form a triangle when laid end to end with the 6cm and 9cm rods.