Question

With a triangle of perimeter 16, how many traingles are possible

Answer 1

Answer:

5

Step-by-step explanation:

A triangle can be formed with side lengths a, b, and c.  

In every step, we need to keep in mind the Triangle Inequality, that any side (c) must always be greater than the sum of other two sides (a+b) and as well, smaller than the magnitude of difference of other two sides (|a-b|)

⇒ |a−b| < c < a+b

Thus when a + b + c = 16, the following are possible distinct triangles,

(2,7,7), (3,6,7), (4,6,6), (4,5,7), (5,5,6)