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.

Explanation:

Step1: Check the triangle inequality for 11, 16, 7

The triangle inequality states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(a + b>c\), \(a + c>b\), and \(b + c>a\).
For \(a = 7\), \(b=11\), \(c = 16\):
\(7+11=18>16\), \(7 + 16=23>11\), \(11+16=27>7\)

Step2: Check the triangle inequality for 17, 21, 12

For \(a = 12\), \(b = 17\), \(c=21\):
\(12 + 17=29>21\), \(12+21=33>17\), \(17+21=38>12\)

Step3: Check the triangle inequality for 20, 3, 18

For \(a = 3\), \(b = 18\), \(c = 20\):
\(3+18=21>20\), \(3 + 20=23>18\), \(18+20=38>3\)

Answer:

Sides	Triangle	Not a Triangle
17, 21, 12	\( \text{Triangle}\)
20, 3, 18	\( \text{Triangle}\)