Answer:
5, 15, 19}
According to the triangle i
nequality theorem, the sum of the lengths of any two sides of a ∆ must be greater than the length of the third side.
Thus, any of the given sets of numbers will represent the 3 sides of a ∆, if the following condition is satisfied:
a + b > c
b + c > a
a + c > b
Where a and b are the smaller side lengths, and c is the length of the longest side.
Let's check each set of numbers given to see if any satisfies this condition.
✍️Option 1: {6, 20, 28}
6 + 20 is not greater than 28
20 + 28 > 6
6 + 28 > 20
❌This set of numbers does not represent the sides of a ∆.
✍️Option 2: {4, 11, 15}
4 + 11 = 15
11 + 15 > 4
4 + 15 > 11
❌This set of numbers does not represent the sides of a ∆.
Option 3: {9, 19, 30}
9 + 19 is not greater than 30
19 + 30 > 9
9 + 30 > 19
❌This set of numbers does not represent the sides of a ∆
Option 4: {5, 15, 19}
5 + 15 > 19
15 + 19 > 5
5 + 19 > 15
✅This set of numbers does not represent the sides of a ∆
Only option 4, satisfied the condition stated earlier, therefore, based on the triangle inequality theorem, {5, 15, 19}, is the set of numbers that represents the 3 sides of a triangle.
Step-by-step explanation:
