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Can the sides of a triangle have lengths $1$ , $3$ , and $3$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Triangle inequality

Full solution

Q. Can the sides of a triangle have lengths

1

,

3

, and

3

?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Triangle Inequality Theorem: To determine if these side lengths can form a triangle, we need to check the triangle inequality theorem. The 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 $1 + 3 > 3$ : Check if $1 + 3 > 3$ . Calculation: $1 + 3 = 4$ , and $4 > 3$ , so this condition is satisfied.
Check $3 + 3 > 1$ : Check if $3 + 3 > 1$ . Calculation: $3 + 3 = 6$ , and $6 > 1$ , so this condition is also satisfied.
Check $1 + 3 > 3$ : Check if $1 + 3 > 3$ . Calculation: $1 + 3 = 4$ , and $4 > 3$ , so this condition is satisfied.

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