Which of the following sets of numbers could not represent the three sides of a triangle? $\newline$ $\{13,22,36\}$ $\newline$ $\{8,18,25\}$ $\newline$ $\{4,13,15\}$ $\newline$ $\{5,8,12\}$

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Grade 8

Checkpoint: Rational and irrational numbers

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Q. Which of the following sets of numbers could not represent the three sides of a triangle?

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\{13,22,36\}

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\{8,18,25\}

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\{4,13,15\}

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\{5,8,12\}

Recall Triangle Inequality Theorem: Recall 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.
Check Set $\{13,22,36\}$ : Check the set $\{13,22,36\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if 13 + 22 > 36, which is 35 > 36.
Check Set $\{8,18,25\}$ : Since $35$ is not greater than $36$ , the set $\{13,22,36\}$ does not satisfy the Triangle Inequality Theorem and therefore could not represent the sides of a triangle.
Check Set $\{4,13,15\}$ : Check the set $\{8,18,25\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if 8 + 18 > 25, which is 26 > 25.
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.Since all pairs satisfy the Triangle Inequality Theorem, the set $\{8,18,25\}$ could represent the sides of a triangle.
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.Since all pairs satisfy the Triangle Inequality Theorem, the set $\{8,18,25\}$ could represent the sides of a triangle.Check the set $\{4,13,15\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $26$ $0$ , which is $26$ $1$ .
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.Since all pairs satisfy the Triangle Inequality Theorem, the set $\{8,18,25\}$ could represent the sides of a triangle.Check the set $\{4,13,15\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $26$ $0$ , which is $26$ $1$ .Since $26$ $2$ is greater than $26$ $3$ , the set $\{4,13,15\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if $26$ $5$ , which is $26$ $6$ , and $26$ $7$ , which is $26$ $8$ .
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.Since all pairs satisfy the Triangle Inequality Theorem, the set $\{8,18,25\}$ could represent the sides of a triangle.Check the set $\{4,13,15\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $26$ $0$ , which is $26$ $1$ .Since $26$ $2$ is greater than $26$ $3$ , the set $\{4,13,15\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if $26$ $5$ , which is $26$ $6$ , and $26$ $7$ , which is $26$ $8$ .Since all pairs satisfy the Triangle Inequality Theorem, the set $\{4,13,15\}$ could represent the sides of a triangle.
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.Since all pairs satisfy the Triangle Inequality Theorem, the set $\{8,18,25\}$ could represent the sides of a triangle.Check the set $\{4,13,15\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $26$ $0$ , which is $26$ $1$ .Since $26$ $2$ is greater than $26$ $3$ , the set $\{4,13,15\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if $26$ $5$ , which is $26$ $6$ , and $26$ $7$ , which is $26$ $8$ .Since all pairs satisfy the Triangle Inequality Theorem, the set $\{4,13,15\}$ could represent the sides of a triangle.Check the set $\{5,8,12\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $25$ $1$ , which is $25$ $2$ .
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.Since all pairs satisfy the Triangle Inequality Theorem, the set $\{8,18,25\}$ could represent the sides of a triangle.Check the set $\{4,13,15\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $26$ $0$ , which is $26$ $1$ .Since $26$ $2$ is greater than $26$ $3$ , the set $\{4,13,15\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if $26$ $5$ , which is $26$ $6$ , and $26$ $7$ , which is $26$ $8$ .Since all pairs satisfy the Triangle Inequality Theorem, the set $\{4,13,15\}$ could represent the sides of a triangle.Check the set $\{5,8,12\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $25$ $1$ , which is $25$ $2$ .Since $25$ $3$ is greater than $25$ $4$ , the set $\{5,8,12\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if $25$ $6$ , which is $25$ $7$ , and $25$ $8$ , which is $25$ $9$ .
Check Set $\{5,8,12\}$ : Since $26$ is greater than $25$ , the set $\{8,18,25\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if 8 + 25 > 18, which is 33 > 18, and 18 + 25 > 8, which is 43 > 8.Since all pairs satisfy the Triangle Inequality Theorem, the set $\{8,18,25\}$ could represent the sides of a triangle.Check the set $\{4,13,15\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $26$ $0$ , which is $26$ $1$ .Since $26$ $2$ is greater than $26$ $3$ , the set $\{4,13,15\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if $26$ $5$ , which is $26$ $6$ , and $26$ $7$ , which is $26$ $8$ .Since all pairs satisfy the Triangle Inequality Theorem, the set $\{4,13,15\}$ could represent the sides of a triangle.Check the set $\{5,8,12\}$ to see if it satisfies the Triangle Inequality Theorem. $\newline$ Calculate if $25$ $1$ , which is $25$ $2$ .Since $25$ $3$ is greater than $25$ $4$ , the set $\{5,8,12\}$ satisfies the Triangle Inequality Theorem for this pair of sides. We must also check the other pairs. $\newline$ Calculate if $25$ $6$ , which is $25$ $7$ , and $25$ $8$ , which is $25$ $9$ .Since all pairs satisfy the Triangle Inequality Theorem, the set $\{5,8,12\}$ could represent the sides of a triangle.