Question

In the figure below, triangles ABC and XYZ are similar. Find x.

Answer 1

6

8

10

4

Answer 2

Similar means that they are not necessarily congruent (the same), but they are proportional.
If a triangle has the sides 1, 2, 3 then a triangle that is similar to that triangle would have any multiple of those sides. For example, if every side was doubled in length, giving you 2, 4, 6, then that triangle would be similar to the original triangle!
So the triangles are similar; the one on the left is 1/2 or 3 or some number we don't know times bigger or smaller than the triangle on the right. We find this number through a simple comparison:
ABC is similar to XYZ, so AB is similar to XY
20 is similar to 10
That means that ABC is twice the size of XYZ!
Also, because ABC is similar to XYZ, BC is similar to YZ (which is x).
Remember though, BC is twice the size of YZ (which is x) because we figured out the proportion.
So this means that BC=2*x
But we know that BC=16.
So 16=2x
Divide both sides by 2
x=8

Answer 3

@ijakez that was alot but i understand thank you.