To determine the type of triangle formed by the side lengths of 4, 7, and 9, we first need to check if these lengths can form a triangle using the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let’s apply this to our side lengths:
- 4 + 7 > 9: true (11 > 9)
- 4 + 9 > 7: true (13 > 7)
- 7 + 9 > 4: true (16 > 4)
Since all three conditions are satisfied, a triangle with these side lengths can indeed exist.
Next, we will classify the triangle. The type of triangle can be determined by comparing the lengths of its sides. In this case:
- 4 is the smallest side,
- 7 is the medium side,
- 9 is the longest side.
Since all three sides are of different lengths, this triangle is classified as a scalene triangle.
In summary, a triangle with side lengths of 4, 7, and 9 is a scalene triangle because all sides are of different lengths.