Question

determine whether the side lengths could form a triangle. see example 5. 22. 13, 15, 9 23. 8, 15, 7 24. 35, 20, 11 25. 65, 32, 40

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (where \(c\geq a\) and \(c\geq b\)), check if \(a + b>c\).

For 13, 15, 9:

Let \(a = 9\), \(b = 13\), \(c = 15\).
\(9+13=22>15\)
Let \(a = 9\), \(b = 15\), \(c = 13\).
\(9 + 15=24>13\)
Let \(a=13\), \(b = 15\), \(c = 9\).
\(13+15=28>9\)

For 8, 15, 7:

Let \(a = 7\), \(b = 8\), \(c = 15\).
\(7+8=15
ot>15\)

For 35, 20, 11:

Let \(a = 11\), \(b = 20\), \(c = 35\).
\(11+20=31
ot>35\)

For 65, 32, 40:

Let \(a = 32\), \(b = 40\), \(c = 65\).
\(32 + 40=72>65\)
Let \(a = 32\), \(b = 65\), \(c = 40\).
\(32+65=97>40\)
Let \(a=40\), \(b = 65\), \(c = 32\).
\(40+65=105>32\)

Answer:

1. Yes, the side lengths 13, 15, 9 can form a triangle.
2. No, the side lengths 8, 15, 7 cannot form a triangle.
3. No, the side lengths 35, 20, 11 cannot form a triangle.
4. Yes, the side lengths 65, 32, 40 can form a triangle.