Question

Prove that in any triangle the length of a side is less than the half of the perimeter in statement reason format.

Answer 1

Answer:

Proved

Step-by-step explanation:

I am going to pose c as the largest side in a random triangle

If so then remember that, by the triangle inequality, a + b > c. Let's start from there...

Statement:                         |                                  Reasoning:

1. a + b > c                                                             1. Triangle Inequality

2. a + b + c > c + c (adding c on both sides),      2. Algebra + Def. Of Perimeter

   a + b + c > 2c (simplified)

   Perimeter > 2c (definition of perimeter)

   c < 1/2 * Perimeter