SOLUTION: please can you help with this question I have tried and failed. Nick has six sticks of the following lengths:3cm, 3cm, 5cm, 9cm, 11cm and 13 cm. how many different triangles can he

Question 808529: please can you help with this question I have tried and failed. Nick has six sticks of the following lengths:3cm, 3cm, 5cm, 9cm, 11cm and 13 cm. how many different triangles can he make using three of these stick?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Three side lengths chosen from the given set may or may not make a triangle.
because a side cannot be longer than the sum of the lengths of the other two sides
(The shortest distance between 2 points is a straight line, so going from one vertex to another along one side of the triangle is shorter than going the other way around through the third vertex).

That requirement seriously limits your choices.
If your shorter side measures 3cm, and you decide to usr the other 3-cm stick, the longest side must be shorter than
3cm+3cm = 6cm.
That makes 3, 3, and 5 cm your only choice.
With a 3cm stick and a 5 cm stick,
you would need a third stick shorter than 8cm,
so that does not give you any additional triangle.
If the shorter sides are 3 and 9cm long,
the third side must be shorter than 12cm,
giving you a second possible triangle with sides
3, 9, and 11cm long.
With the 3, 11, and 13-cm sticks,
you can make a third triangle.
Without the 3-cm sticks, you can make 3 more triangles.
One will have sides 5, 9 and 11cm long.
Another one will have sides 5, 9 and 13 cm long.
The last of your possible triangles has sides measuring 9, 11, and 13cm.
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