Question

How many triangles can be made out of $15$ matchsticks?

• A. $17$
• B. $7$
• C. $6$
• D. $3$

Answer 1

Answer: (B)

$7$

We can determine a pattern from the image to find the number of matchsticks required for making a fixed number of triangles.

From the image, we can see the after the $1st$ triangle (which need $3$ matchsticks) we need only $2$ matchsticks to make another Rhombus.

So for making $(x+1)$ triangles, we need:

$3+2\times \left(x\right)$ matchsticks.

Now according to questions:

$=>3+2\times x=15$

$=>2\times x=12=>x=6$.

So number of triangles $=x+1=6+1=7$