Can the sides of a triangle have lengths 3, 7, and 9? Choices: (A)yes (B)no

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. Check 3 + 7: Check if 3 + 7 > 9. Calculation: 3 + 7 = 10, and 10 > 9, so this part is true. Check 3 + 9: Check if 3 + 9 > 7. Calculation: 3 + 9 = 12, and 12 > 7, so this part is true too. Check 7 + 9: Check if 7 + 9 > 3. Calculation: 7 + 9 = 16, and 16 > 3, so this part is also true.

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Can the sides of a triangle have lengths $3$ , $7$ , and $9$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Q. Can the sides of a triangle have lengths

3

7

, and

9

\newline

Choices:

\newline

(A) yes

\newline

(B) no

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.
Check $3 + 7$ : Check if 3 + 7 > 9. Calculation: $3 + 7 = 10$ , and 10 > 9, so this part is true.
Check $3 + 9$ : Check if 3 + 9 > 7. Calculation: $3 + 9 = 12$ , and 12 > 7, so this part is true too.
Check $7 + 9$ : Check if 7 + 9 > 3. Calculation: $7 + 9 = 16$ , and 16 > 3, so this part is also true.