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 8.7, 11.8, 3.1 8, 14, 9 9, 18, 12 8, 7, 9

Explanation:

Step1: Check triangle inequality for \(8.7, 11.8, 3.1\)

Check if \(a + b>c\), \(a + c>b\) and \(b + c>a\). Let \(a = 3.1\), \(b=8.7\), \(c = 11.8\).
\(a + b=3.1+8.7 = 11.8\), and \(11.8
ot>11.8\) (since \(a + b=c\)).

Step2: Check triangle inequality for \(8,14,9\)

Let \(a = 8\), \(b = 9\), \(c=14\).
\(a + b=8 + 9=17>14\), \(a + c=8+14 = 22>9\), \(b + c=9 + 14=23>8\).

Step3: Check triangle inequality for \(9,18,12\)

Let \(a = 9\), \(b = 12\), \(c = 18\).
\(a + b=9+12 = 21>18\), \(a + c=9+18=27>12\), \(b + c=12 + 18=30>9\).

Step4: Check triangle inequality for \(8,7,9\)

Let \(a = 7\), \(b = 8\), \(c = 9\).
\(a + b=7+8 = 15>9\), \(a + c=7+9=16>8\), \(b + c=8 + 9=17>7\).

Answer:

• \(8.7, 11.8, 3.1\): Cannot be side lengths of a triangle
• \(8,14,9\): Can be side lengths of a triangle
• \(9,18,12\): Can be side lengths of a triangle
• \(8,7,9\): Can be side lengths of a triangle