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Can the sides of a triangle have lengths $3$ , $6$ , and $7$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Triangle inequality

Full solution

Q. Can the sides of a triangle have lengths

3

,

6

, 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 $3 + 6 > 7$ : Check if $3 + 6 > 7$ . Calculation: $3 + 6 = 9$ , and $9 > 7$ , so this part is true.
Check $3 + 7 > 6$ : Check if $3 + 7 > 6$ . Calculation: $3 + 7 = 10$ , and $10 > 6$ , so this part is true too.
Check $6 + 7 > 3$ : Check if $6 + 7 > 3$ . Calculation: $6 + 7 = 13$ , and $13 > 3$ , so this part is also true.

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