Help!!! I don’t know what to do

The triangles are similar. what is the value of x? show your work.

Apsychology student wishes to investigate differences in political opinions between business majors and political science majors at her college. she randomly selects 100 students from the 260 business majors and 100 students from the 180 political science majors. does this sampling plan result in a simple random sample? why or why not? no, because each group of 200 students in the sample does not have the same chance of being selected. yes, because each group of 200 students in the sample has the same chance of being selected. no, because each individual student does not have an equal chance of being selected. yes, because each individual student has the same chance of being selected.

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.