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Which of the following sets of numbers could represent the three sides of a triangle? {12,23,32} {13,17,30} {14,27,41} {12,21,35}

Which of the following sets of numbers could represent the three sides of a triangle?\newline{12,23,32} \{12,23,32\} \newline{13,17,30} \{13,17,30\} \newline{14,27,41} \{14,27,41\} \newline{12,21,35} \{12,21,35\}

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Q. Which of the following sets of numbers could represent the three sides of a triangle?\newline{12,23,32} \{12,23,32\} \newline{13,17,30} \{13,17,30\} \newline{14,27,41} \{14,27,41\} \newline{12,21,35} \{12,21,35\}
  1. Understand Triangle Inequality Theorem: Identify the Triangle Inequality Theorem, which 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. Test First Set of Numbers: Test the first set of numbers 12,23,32{12, 23, 32} to see if they satisfy the Triangle Inequality Theorem.\newlineCheck if 12+23>3212 + 23 > 32, 12+32>2312 + 32 > 23, and 23+32>1223 + 32 > 12.\newlinePerform the calculations: 12+23=3512 + 23 = 35, 12+32=4412 + 32 = 44, 23+32=5523 + 32 = 55.\newlineAll three conditions are true: 35>3235 > 32, 44>2344 > 23, and 55>1255 > 12.
  3. Test Second Set of Numbers: Test the second set of numbers {13,17,30}\{13, 17, 30\} to see if they satisfy the Triangle Inequality Theorem.\newlineCheck if 13+17>3013 + 17 > 30, 13+30>1713 + 30 > 17, and 17+30>1317 + 30 > 13.\newlinePerform the calculations: 13+17=3013 + 17 = 30, 13+30=4313 + 30 = 43, 17+30=4717 + 30 = 47.\newlineThe first condition is not true: 13+17=3013 + 17 = 30 is not greater than 3030.\newlineThis set of numbers cannot represent the sides of a triangle.
  4. Test Third Set of Numbers: Test the third set of numbers {14,27,41}\{14, 27, 41\} to see if they satisfy the Triangle Inequality Theorem.\newlineCheck if 14+27>4114 + 27 > 41, 14+41>2714 + 41 > 27, and 27+41>1427 + 41 > 14.\newlinePerform the calculations: 14+27=4114 + 27 = 41, 14+41=5514 + 41 = 55, 27+41=6827 + 41 = 68.\newlineThe first condition is not true: 14+27=4114 + 27 = 41 is not greater than 4141.\newlineThis set of numbers cannot represent the sides of a triangle.
  5. Test Fourth Set of Numbers: Test the fourth set of numbers {12,21,35}\{12, 21, 35\} to see if they satisfy the Triangle Inequality Theorem.\newlineCheck if 12+21>3512 + 21 > 35, 12+35>2112 + 35 > 21, and 21+35>1221 + 35 > 12.\newlinePerform the calculations: 12+21=3312 + 21 = 33, 12+35=4712 + 35 = 47, 21+35=5621 + 35 = 56.\newlineThe first condition is not true: 12+21=3312 + 21 = 33 is not greater than 3535.\newlineThis set of numbers cannot represent the sides of a triangle.

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