Question

determine which of the following sets of numbers could or could not be lengths of sides of a triangle. select the correct option for each set of sides. sides: 19, 13, 16; 9, 33, 13; 21, 18, 3. triangle; not a triangle

Explanation:

Step1: Check the triangle inequality for 19, 13, 16

For three side lengths \(a\), \(b\), \(c\) (where \(a\leq b\leq c\)), the triangle inequality states \(a + b>c\).
Here \(a = 13\), \(b = 16\), \(c = 19\).
\(13+16=29>19\)
\(13 + 19=32>16\)
\(16+19 = 35>13\)

Step2: Check the triangle inequality for 9, 33, 13

Here \(a = 9\), \(b = 13\), \(c = 33\)
\(9+13=22<33\)

Step3: Check the triangle inequality for 21, 18, 3

Here \(a = 3\), \(b = 18\), \(c = 21\)
\(3+18=21\) (the sum of two sides is equal to the third side, not greater)

Answer:

19, 13, 16: Triangle
9, 33, 13: Not a Triangle
21, 18, 3: Not a Triangle