Answer:
5 triangles
Explanation:
Think of it this way, a triangle can be formed only if the sum of any two sides of the triangle is greater than the third side, this is called TRIANGLE INEQUALITY.
a + b > c a + c > b b + c > a
All three must be satisfied for a triangle to form.
Now given your sticks, there are many possible combinations you could use, but only a few of those combinations will satisfy the inequalities.
I will show you two examples, using the two 3 cm sticks and another stick.
3cm + 3cm = 6 cm
This means that the 3rd side needs to be less than 6cm and there's only 1 option, which is the 5 cm because all the other options are greater than 6 cm.
TRIANGLE 1 3 cm, 3cm, 5 cm
(This is also the only triangle a 3 cm and 5 cm combination can make)
Next 3 cm and 9 cm combination:
3 cm + 9 cm = 12 cm
It's third side should have a length less than 12 cm.
TRIANGLE 2 3 cm, 9 cm, 11 cm
Again no other side is less than 12 cm.
So you do this for everything else to determine if a triangle is formed.
