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Can the sides of a triangle have lengths $2$ , $4$ , and $5$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Triangle inequality

Full solution

Q. Can the sides of a triangle have lengths

2

,

4

, and

5

?

\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. The sum of the lengths of any two sides must be greater than the length of the third side.
Check $2 + 4$ : Check if $2 + 4 > 5$ . Calculation: $2 + 4 = 6$ , and $6 > 5$ , so this part is true.
Check $2 + 5$ : Check if $2 + 5 > 4$ . Calculation: $2 + 5 = 7$ , and $7 > 4$ , so this part is true.
Check $4 + 5$ : Check if $4 + 5 > 2$ . Calculation: $4 + 5 = 9$ , and $9 > 2$ , so this part is true.

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