# 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?

Nov 4, 2016

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

$x + 3 + 3 x + 2 + 2 x + 3 = 20$

$6 x + 8 = 20$

$6 x = 12$

$x = 2$

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!