If two triangles are similar, then their corresponding sides are proportional and their corresponding angles are congruent 1. Therefore, we can set up a proportion of the corresponding sides of the two triangles and solve for x.
For example, if we have two similar triangles ABC and EDC with sides AB = 6, BC = 8, AC = 10 and ED = 9, DC = 12, EC = 15 respectively as shown below:
A
/\
/ \
/____\
B C
E
/\
/ \
/____\
D C
We can set up a proportion of the corresponding sides as follows:
AB/ED = BC/DC = AC/EC
6/9 = 8/12 = 10/15
Simplifying this proportion gives us:
2/3 = 2/3 = 2/3
Therefore, x is equal to:
x = EC - DC
x = 15 - 12
x = 3
So in this case, x is equal to 3.
I hope that helps!