Question

Given that triangle ABC, AB=x+3, AC=3x+2, BC=2x+3, and the perimeter of the triangle is 20, how do you show that the triangle is scalene?

Answer 1

We know that the perimeter is given by the sum of the sides, so:

`x + 3 + 3x + 2 + 2x + 3 = 20`

`6x + 8 = 20`

`6x = 12`

`x = 2`

The sides of the triangle hence measure `5`, `8` and `7`. All the sides have different lengths, so the triangle is scalene.

Hopefully this helps!