Which of the following sets of numbers could not represent the three sides of a triangle?
14,24,37
9,21,32
15,30,43
10,19,26
To determine whether a set of numbers could represent the three 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 third side.
Let's analyze each set of numbers:
1) 14, 24, 37:
14 + 24 = 38 > 37
14 + 37 = 51 > 24
24 + 37 = 61 > 14
The set 14, 24, 37 satisfies the triangle inequality theorem and could represent the sides of a triangle.
2) 9, 21, 32:
9 + 21 = 30 < 32
9 + 32 = 41 > 21
21 + 32 = 53 > 9
The set 9, 21, 32 does not satisfy the triangle inequality theorem and could not represent the sides of a triangle.
3) 15, 30, 43:
15 + 30 = 45 < 43
15 + 43 = 58 > 30
30 + 43 = 73 > 15
The set 15, 30, 43 does not satisfy the triangle inequality theorem and could not represent the sides of a triangle.
4) 10, 19, 26:
10 + 19 = 29 < 26
10 + 26 = 36 > 19
19 + 26 = 45 > 10
The set 10, 19, 26 does not satisfy the triangle inequality theorem and could not represent the sides of a triangle.
Therefore, the set of numbers that could not represent the three sides of a triangle is 9, 21, 32.