which of thes cannot representthe length of the sides of a triangle
if the sides are a,b,c, with c being the longest, then you need
c < a+b
To determine which values cannot represent the lengths of the sides of a triangle, we need to 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 consider the given options:
A) 1, 3, 4
B) 2, 6, 8
C) 5, 5, 10
D) 7, 4, 2
By applying the triangle inequality theorem to each option, we can determine if they form a valid triangle:
A) 1 + 3 > 4 (True)
3 + 4 > 1 (True)
4 + 1 > 3 (True)
B) 2 + 6 > 8 (True)
6 + 8 > 2 (True)
8 + 2 > 6 (True)
C) 5 + 5 > 10 (False)
5 + 10 > 5 (True)
10 + 5 > 5 (True)
D) 7 + 4 > 2 (False)
4 + 2 > 7 (False)
2 + 7 > 4 (False)
Using the triangle inequality theorem, we find that option C (5, 5, 10) cannot represent the lengths of the sides of a triangle since the sum of the lengths of the two shorter sides (5 + 5 = 10) is not greater than the length of the longest side (10).
Therefore, the answer is option C cannot represent the length of the sides of a triangle.