Can the sides of a triangle have lengths 3, 5, and 7? Choices: (A)yes (B)no

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. Check 3 + 5 > 7: Check if 3 + 5 > 7. Calculation: 3 + 5 = 8, and 8 > 7, so this part is true. Check 3 + 7 > 5: Check if 3 + 7 > 5. Calculation: 3 + 7 = 10, and 10 > 5, so this part is true too. Check 5 + 7 > 3: Check if 5 + 7 > 3. Calculation: 5 + 7 = 12, and 12 > 3, so this part is also true.

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Can the sides of a triangle have lengths $3$ , $5$ , and $7$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Q. Can the sides of a triangle have lengths

3

5

, and

7

\newline

Choices:

\newline

(A) yes

\newline

(B) no

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.
Check 3 + 5 > 7: Check if 3 + 5 > 7. Calculation: $3 + 5 = 8$ , and 8 > 7, so this part is true.
Check 3 + 7 > 5: Check if 3 + 7 > 5. Calculation: $3 + 7 = 10$ , and 10 > 5, so this part is true too.
Check 5 + 7 > 3: Check if 5 + 7 > 3. Calculation: $5 + 7 = 12$ , and 12 > 3, so this part is also true.