Question

Kendra has an unlimited supply of unbreakable sticks of length $2$, $4$ and $6$ inches. Using these sticks, how many non-congruent triangles can she make if each side is made with a whole stick? two sticks can be joined only at a vertex of the triangle. (a triangle with sides of lengths $4$, $6$, $6$ is an example of one such triangle to be included, whereas a triangle with sides of lengths $2$, $2$, $4$ should not be included. )

Answer 1

5

Explanation:

You want to know the number of non-congruent triangles that can be formed with side lengths of 2 or 4 or 6.

Triangle inequality

The triangle inequality requires the sum of the two shorter sides exceed the length of the longest side. Possible triangles from these side lengths are ...

{2, 2, 2} or {4, 4, 4} or {6, 6, 6} . . . . . an equilateral triangle

{2, 4, 4}

{2, 6, 6}

{4, 4, 6}

{4, 6, 6}

That is, 5 different triangle shapes can be formed from these side lengths.

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