Question

which of the following sets of numbers could be the lengths of the sides of a triangle? 16, 20, 17 9, 3, 17 19, 23, 57 7, 11, 4

Explanation:

Step1: Check triangle inequality for 16,20,17

For a triangle with side lengths \(a\), \(b\), \(c\), the triangle inequality states \(a + b>c\), \(a + c>b\) and \(b + c>a\).
For \(a = 16\), \(b=20\), \(c = 17\):
\(16+20 = 36>17\)
\(16 + 17=33>20\)
\(20+17 = 37>16\)

Step2: Check triangle inequality for 9,3,17

For \(a = 9\), \(b = 3\), \(c=17\):
\(9+3=12<17\)

Step3: Check triangle inequality for 19,23,57

For \(a = 19\), \(b = 23\), \(c = 57\):
\(19+23=42<57\)

Step4: Check triangle inequality for 7,11,4

For \(a = 7\), \(b = 11\), \(c = 4\):
\(7 + 4=11\) (not greater than 11)

Answer:

16,20,17