Answer:
C. x = 1/2
Explanation:
First, let's find the perimeter of each triangle. To do this, we just have to add up the lengths of all the sides together - not too bad. Let's start with Triangle ABC. (x + 2) + (2x) + (x) = x + 2x + x + 2 = 4x + 2. So, 4x + 2 is the perimeter of Triangle ABC.
Now, let's take a look at Triangle LMN. (3x - 1) + (4x + 2) + (3x) = 3x + 4x + 3x - 1 + 2 = 10x + 1. 10x - 1 is the perimeter of Triangle LMN.
So, we want to find the value of x for the perimeters to be congruent, so let's go ahead and make those two expressions equal and see what happens.
10x - 1 = 4x + 2
6x - 1 = 2
6x = 3
x = 1/2
So, x has to be 1/2 for the perimeters to be congruent. Hopefully that's helpful. :)