Which of the following sets of numbers could represent the three sides of a triangle? $\newline$ $\{13,22,32\}$ $\newline$ $\{11,22,33\}$ $\newline$ $\{14,20,36\}$ $\newline$ $\{15,21,37\}$

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Grade 8

Checkpoint: Rational and irrational numbers

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Q. Which of the following sets of numbers could represent the three sides of a triangle?

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\{13,22,32\}

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\{11,22,33\}

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\{14,20,36\}

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\{15,21,37\}

Recall Triangle Inequality Theorem: Recall the Triangle Inequality Theorem. $\newline$ The Triangle Inequality 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.
Apply Theorem to Set $\{13,22,32\}$ : Apply the Triangle Inequality Theorem to the first set $\{13,22,32\}$ . $\newline$ Check if 13 + 22 > 32, 13 + 32 > 22, and 22 + 32 > 13. $\newline$ $13 + 22 = 35$ , which is greater than $32$ . $\newline$ $13 + 32 = 45$ , which is greater than $22$ . $\newline$ $22 + 32 = 54$ , which is greater than $\{13,22,32\}$ $0$ . $\newline$ All conditions are satisfied, so $\{13,22,32\}$ could represent the sides of a triangle.
Apply Theorem to Set $\{11,22,33\}$ : Apply the Triangle Inequality Theorem to the second set $\{11,22,33\}$ . Check if 11 + 22 > 33, 11 + 33 > 22, and 22 + 33 > 11. $11 + 22 = 33$ , which is not greater than $33$ . This set does not satisfy the Triangle Inequality Theorem, so $\{11,22,33\}$ cannot represent the sides of a triangle.
Apply Theorem to Set $\{14,20,36\}$ : Apply the Triangle Inequality Theorem to the third set $\{14,20,36\}$ . Check if 14 + 20 > 36, 14 + 36 > 20, and 20 + 36 > 14. $14 + 20 = 34$ , which is not greater than $36$ . This set does not satisfy the Triangle Inequality Theorem, so $\{14,20,36\}$ cannot represent the sides of a triangle.
Apply Theorem to Set ${15,21,37}$ : Apply the Triangle Inequality Theorem to the fourth set ${15,21,37}$ . Check if 15 + 21 > 37, 15 + 37 > 21, and 21 + 37 > 15. $15 + 21 = 36$ , which is not greater than $37$ . This set does not satisfy the Triangle Inequality Theorem, so ${15,21,37}$ cannot represent the sides of a triangle.