Question

Suppose you have 3 pieces of string measuring 6 inches, 9 inches, and 12 inches. How many unique triangles can you form with these pieces of string?

*0
*1
*2
*infinitely many

Answer 1

2

Explanation:

This can be easily understood with the triangle inequality theorem, which tells us that "the sum of any two side of a triangle is always greater than the third side". Let's check:

• Is 6+9 greater than 12? Yes!
• Is 6+12 greater than 9? Yes!
• Is 9+12 greater than 6? Yes!

So, first of all, it is possible to create triangle(s). Moreover, it also says that "If longest side is less than sum of the other two sides and those two sides are NOT equal, then we have two congruent triangles which are mirror images of each other".

Hence we can create 2 triangles.