Question

part 1: triangle inequality theorem (1 - 10)
determine whether the given side lengths can form a triangle. if they can, slate \yes.\ if not, slate
o.\
(remember the sum of any two sides must be greater than the third side.)

1. 5.7 10
2. 3.4 8
3. 9.9 18
4. 6.8 9
5. 10.5 4
6. 12.7 6
7. 15.10 5
8. 8.8 12
9. 2.3 4
10. 11.4 7

Explanation:

Step1: Check the first set of side lengths \(5.7,10,2.3\)

• Check \(5.7 + 2.3>10\): \(5.7+2.3 = 8<10\)

Step2: Check the second set of side lengths \(5.7,10,4.8\)

• Check \(5.7+4.8>10\): \(5.7 + 4.8=10.5>10\)
• Check \(5.7+10>4.8\): \(5.7+10 = 15.7>4.8\)
• Check \(10 + 4.8>5.7\): \(10+4.8=14.8>5.7\)

Step3: Check the third set of side lengths \(5.7,10,3.9\)

• Check \(5.7+3.9>10\): \(5.7+3.9 = 9.6<10\)

Step4: Check the fourth set of side lengths \(5.7,10,6.8\)

• Check \(5.7+6.8>10\): \(5.7+6.8=12.5>10\)
• Check \(5.7+10>6.8\): \(5.7+10 = 15.7>6.8\)
• Check \(10+6.8>5.7\): \(10 + 6.8=16.8>5.7\)

Step5: Check the fifth set of side lengths \(5.7,10,10.5\)

• Check \(5.7+10>10.5\): \(5.7+10=15.7>10.5\)
• Check \(5.7+10.5>10\): \(5.7+10.5 = 16.2>10\)
• Check \(10+10.5>5.7\): \(10+10.5=20.5>5.7\)

Step6: Check the sixth set of side lengths \(5.7,10,8.8\)

• Check \(5.7+8.8>10\): \(5.7+8.8=14.5>10\)
• Check \(5.7+10>8.8\): \(5.7+10 = 15.7>8.8\)
• Check \(10+8.8>5.7\): \(10+8.8=18.8>5.7\)

Step7: Check the seventh set of side lengths \(5.7,10,9.2\)

• Check \(5.7+9.2>10\): \(5.7+9.2=14.9>10\)
• Check \(5.7+10>9.2\): \(5.7+10 = 15.7>9.2\)
• Check \(10+9.2>5.7\): \(10+9.2=19.2>5.7\)

Step8: Check the eighth set of side lengths \(5.7,10,10.1\)

• Check \(5.7+10>10.1\): \(5.7+10=15.7>10.1\)
• Check \(5.7+10.1>10\): \(5.7+10.1 = 15.8>10\)
• Check \(10+10.1>5.7\): \(10+10.1=20.1>5.7\)

Step9: Check the ninth set of side lengths \(5.7,10,11.4\)

• Check \(5.7+10>11.4\): \(5.7+10=15.7>11.4\)
• Check \(5.7+11.4>10\): \(5.7+11.4 = 17.1>10\)
• Check \(10+11.4>5.7\): \(10+11.4=21.4>5.7\)

Step10: Check the tenth set of side lengths \(5.7,10,7\)

• Check \(5.7+7>10\): \(5.7+7=12.7>10\)
• Check \(5.7+10>7\): \(5.7+10 = 15.7>7\)
• Check \(10+7>5.7\): \(10+7=17>5.7\)

Answer:

1. No; 2. Yes; 3. No; 4. Yes; 5. Yes; 6. Yes; 7. Yes; 8. Yes; 9. Yes; 10. Yes