# Thread: Max Numbers of Different Triangles

1. ## Max 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?

2. Originally Posted by magentarita
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?
You are supposed to know the triangle inequality. If the sides of a triangle are a, b and c then the inequality

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

must be satisfied.

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

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.

3. ## earboth

Originally Posted by earboth
You are supposed to know the triangle inequality. If the sides of a triangle are a, b and c then the inequality

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

must be satisfied.

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