Please help me out. I couldn’t figure it out.

The triangles are similar. what is the value of x? x=

Can someone check if i did this right since i really want to make sure it’s correct. if you do you so much

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?