A box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. What is the maximum number of different triangles that can be made using these rods as sides?

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- Sep 26th 2008, 05:21 AMmagentaritaMax Numbers of Different Triangles
A box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. What is the maximum number of different triangles that can be made using these rods as sides?

- Sep 27th 2008, 04:23 AMearboth
You are supposed to know the triangle inequality. If the sides of a triangle are a, b and c then the inequality

$\displaystyle a+b>c~\wedge~a+c>b~\wedge~b+c>a$

must be satisfied.

With your values you get:

$\displaystyle \begin{array}{cccc}a&b&c& \\2&3&4&OK\\2&3&5&No,\ but\ why?\\2&4&5&OK \\ 3&4&5&OK\end{array}$

So I've got 3 triangles maximum. Probably I've forgotten one or two combinations but I hope you know now how to do this question. - Sep 27th 2008, 04:25 AMmagentaritaearboth