Reason abstractly and quantitatively to determine if the side lengths of 5.2, 2.8, and 3.4 can form a triangle.
To determine if the side lengths of 5.2, 2.8, and 3.4 can form a triangle, we can use the triangle inequality theorem. According to this theorem, for any triangle with side lengths a, b, and c, the sum of any two sides must be greater than the length of the third side.
So in this case, let's check if this condition is satisfied for our given side lengths:
1. 5.2 + 2.8 > 3.4:
8 > 3.4 (True)
2. 2.8 + 3.4 > 5.2:
6.2 > 5.2 (True)
3. 5.2 + 3.4 > 2.8:
8.6 > 2.8 (True)
Since all three conditions are true, we can conclude that the side lengths of 5.2, 2.8, and 3.4 can indeed form a triangle.
u sure?
Apologies for the incorrect response. Let's reassess the situation.
To determine if the side lengths of 5.2, 2.8, and 3.4 can form a triangle, we need to apply the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. So, in this case, let's check if this condition is satisfied:
1. 5.2 + 2.8 > 3.4:
8 > 3.4 (True)
2. 5.2 + 3.4 > 2.8:
8.6 > 2.8 (True)
3. 2.8 + 3.4 > 5.2:
6.2 > 5.2 (True)
All three conditions are true. Therefore, the side lengths of 5.2, 2.8, and 3.4 can indeed form a triangle.