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Can the sides of a triangle have lengths 33, 55, and 77?\newlineChoices:\newline(A) yes\newline(B) no

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Full solution

Q. Can the sides of a triangle have lengths 33, 55, and 77?\newlineChoices:\newline(A) yes\newline(B) no
  1. Check Triangle Inequality Theorem: To determine if these can be the sides of a triangle, we need to check the triangle inequality theorem. The sum of the lengths of any two sides must be greater than the length of the third side.
  2. Check 3+5>73 + 5 > 7: Check if 3+5>73 + 5 > 7. Calculation: 3+5=83 + 5 = 8, and 8>78 > 7, so this part is true.
  3. Check 3+7>53 + 7 > 5: Check if 3+7>53 + 7 > 5. Calculation: 3+7=103 + 7 = 10, and 10>510 > 5, so this part is true too.
  4. Check 5+7>35 + 7 > 3: Check if 5+7>35 + 7 > 3. Calculation: 5+7=125 + 7 = 12, and 12>312 > 3, so this part is also true.

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