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To determine whether it is possible to form a triangle with the side lengths of 3, 7, and 8, we need to apply the **triangle inequality theorem**. The theorem states that for three side lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

For the sides 3, 7, and 8, we check the following inequalities:

1. \( 3 + 7 > 8 \) → \( 10 > 8 \) (True)
2. \( 3 + 8 > 7 \) → \( 11 > 7 \) (True)
3. \( 7 + 8 > 3 \) → \( 15 > 3 \) (True)

Since all three conditions are satisfied, it **is** possible to form a triangle with the side lengths 3, 7, and 8. Therefore, the answer is **yes**.

Would you like more details on the triangle inequality theorem, or do you have any questions?

Here are some related questions:
1. What is the triangle inequality theorem in detail?
2. How do we classify triangles based on their sides (equilateral, isosceles, scalene)?
3. What happens if the triangle inequality does not hold for three side lengths?
4. Can a triangle be formed if two of its sides are equal in length?
5. How does the triangle inequality apply in different geometric contexts, such as in non-Euclidean spaces?

**Tip**: Whenever solving for possible triangle formations, always check all three inequalities carefully to ensure accuracy.

Is it possible to create a triangle with the following side lengths: 3, 7, 8?

Explore whether a triangle can be formed with side lengths 3, 7, and 8 using the Triangle Inequality Theorem. Learn how to apply the theorem and understand the conditions needed for triangle formation. Suitable for students in Grades 6-8.

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