4. find the value of each variable for the right triangles. make sure all answers are in reduced radical form. show your work.

For this case, the first thing you should keep in mind is the Pythagorean theorem to find the required variables.
 Triangle number 1: 
 t ^ 2 + 12 ^ 2 = 13 ^ 2
 From here, we clear the value of t:
 t = root (13 ^ 2 - 12 ^ 2)
 t = 5
 Triangle number 2:
 x ^ 2 = 6 ^ 2 + 9 ^ 2
 From here, we clear the value of x:
 x = root (6 ^ 2 + 9 ^ 2)
 x = root (117)
 x = root (9 * 13)
 x = 3raiz (13)
  
 The value of the variables searched is: 
 t = 5
 x = 3raiz (13)

It is going to be the third choice