Question

for each set of three lengths, determine if they can be the side lengths of a triangle. lengths can be side lengths of a triangle cannot be side lengths of a triangle 18, 9, 28 29, 17, 6 11.8, 19.8, 8.5 21, 6, 6

Explanation:

Step1: Check triangle inequality for \(18,9,28\)

The triangle inequality states that for three side lengths \(a,b,c\), \(a + b>c\), \(a + c>b\) and \(b + c>a\).
For \(a = 9\), \(b = 18\), \(c = 28\):
\(9+18=27<28\)

Step2: Check triangle inequality for \(29,17,6\)

For \(a = 6\), \(b = 17\), \(c = 29\):
\(6 + 17=23<29\)

Step3: Check triangle inequality for \(11.8,19.8,8.5\)

For \(a = 8.5\), \(b = 11.8\), \(c = 19.8\):
\(8.5+11.8 = 20.3>19.8\)
\(8.5+19.8=28.3>11.8\)
\(11.8 + 19.8=31.6>8.5\)

Step4: Check triangle inequality for \(21,6,6\)

For \(a = 6\), \(b = 6\), \(c = 21\):
\(6+6 = 12<21\)

Answer:

• \(18,9,28\): Cannot be side lengths of a triangle
• \(29,17,6\): Cannot be side lengths of a triangle
• \(11.8,19.8,8.5\): Can be side lengths of a triangle
• \(21,6,6\): Cannot be side lengths of a triangle