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Can the sides of a triangle have lengths 33, 77, and 99?\newlineChoices:\newline(A) yes\newline(B) no

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Full solution

Q. Can the sides of a triangle have lengths 33, 77, and 99?\newlineChoices:\newline(A) yes\newline(B) no
  1. Triangle Inequality Theorem: To determine if these can be the sides of a triangle, we need to check the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
  2. Check 3+73 + 7: Check if 3+7>93 + 7 > 9. Calculation: 3+7=103 + 7 = 10, and 10>910 > 9, so this part is true.
  3. Check 3+93 + 9: Check if 3+9>73 + 9 > 7. Calculation: 3+9=123 + 9 = 12, and 12>712 > 7, so this part is true too.
  4. Check 7+97 + 9: Check if 7+9>37 + 9 > 3. Calculation: 7+9=167 + 9 = 16, and 16>316 > 3, so this part is also true.

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