Since the teacher's desk is similar to the student's desk, their corresponding sides are proportional.
Let x be the width of the teacher's desk. Then, we can set up the following proportion:
student desk length : student desk width :: teacher desk length : teacher desk width
or
30 : 18 :: 50 : x
To solve for x, we can cross-multiply:
30x = 18 * 50
30x = 900
x = 30
Therefore, the width of the teacher's desk is 30 inches