Which set of three side lengths will NOT form a triangle?
A
17, 12, 6
B
25, 38, 13
C
36, 14, 27
D
39, 44, 6
B
sum of any 2 sides of a triangle must be greater than the third side
like what the?? B THOUGH.. Its B :/
To determine if a set of three side lengths will form a triangle, we can apply 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 remaining side.
Let's proceed with each set of side lengths provided:
A: 17, 12, 6
To check if these lengths form a triangle, we need to confirm that the sum of any two sides is greater than the length of the remaining side.
- Sum of 17 and 12 = 29, which is greater than 6.
- Sum of 12 and 6 = 18, which is greater than 17.
- Sum of 17 and 6 = 23, which is greater than 12.
Since all three combinations satisfy the triangle inequality, this set of side lengths will form a triangle.
B: 25, 38, 13
Let's perform the same check:
- Sum of 25 and 38 = 63, which is greater than 13.
- Sum of 38 and 13 = 51, which is greater than 25.
- Sum of 25 and 13 = 38, which is less than 38.
In this case, the sum of the two smaller sides is not greater than the longest side (25), so this set of side lengths will not form a triangle.
C: 36, 14, 27
Checking the combinations:
- Sum of 36 and 14 = 50, which is greater than 27.
- Sum of 14 and 27 = 41, which is greater than 36.
- Sum of 36 and 27 = 63, which is greater than 14.
Since all three combinations satisfy the triangle inequality, this set of side lengths will form a triangle.
D: 39, 44, 6
Last set, let's apply the triangle inequality:
- Sum of 39 and 44 = 83, which is greater than 6.
- Sum of 44 and 6 = 50, which is greater than 39.
- Sum of 39 and 6 = 45, which is greater than 44.
Again, all three combinations satisfy the triangle inequality, so this set of side lengths will form a triangle.
In conclusion, the set of side lengths that will NOT form a triangle is B: 25, 38, 13.