Question

Question

Which of the following sets of numbers could not represent the three sides of a triangle?
Answer
{8, 14, 20}
{6,8,14}
{4,6,7}
O{4, 14, 17}
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Answer 1

The set {8, 14, 20} could not represent the sides of a triangle.

Step-by-step explanation:

To determine if a set of numbers can represent the sides of a triangle, we 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 remaining side. Let's test each set of numbers:

1. {8, 14, 20}: The sum of the two smaller sides (8 + 14 = 22) is not greater than the longest side (20). Therefore, this set cannot represent the sides of a triangle.
2. {6, 8, 14}: The sum of the two smaller sides (6 + 8 = 14) is equal to the length of the remaining side (14). Therefore, this set represents a degenerate triangle, which is a triangle with all three sides lying on the same line.
3. {4, 6, 7}: The sum of the two smaller sides (4 + 6 = 10) is greater than the length of the remaining side (7). Therefore, this set can represent the sides of a triangle.
4. {4, 14, 17}: The sum of the two smaller sides (4 + 14 = 18) is greater than the length of the remaining side (17). Therefore, this set can represent the sides of a triangle.

In conclusion, the set of numbers that could not represent the three sides of a triangle is {8, 14, 20}.

Learn more about Triangle inequality theorem