Reason abstractly and quantitatively to determine if the side lengths of 5.2, 2.8, and 3.4 can form a triangle.
No, they do not because 2.8 is not greater than the difference of b−c.
No, they do not because 3.4 is not greater than the difference of b−c.
No, they do not because 5.2 is not greater than the difference of b−c.
Yes, they do form a triangle.
No, they do not 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, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's assume that 5.2 is the length of side "a", 2.8 is the length of side "b", and 3.4 is the length of side "c".
To determine if these side lengths can form a triangle, we need to check if the following conditions are met:
1) a + b > c
2) a + c > b
3) b + c > a
Using the given side lengths, we can substitute the values and test the conditions:
1) 5.2 + 2.8 > 3.4
8 > 3.4 (This condition is met)
2) 5.2 + 3.4 > 2.8
8.6 > 2.8 (This condition is met)
3) 2.8 + 3.4 > 5.2
6.2 > 5.2 (This condition is met)
Since all three conditions are met, the side lengths of 5.2, 2.8, and 3.4 can form a triangle.