EOFError: EOF when reading a line

convert your inputs to ints:

width = int(input())
height = int(input())

Use a try / except block to get rid of the EOF error.

try:
    width = input()
    height = input()
    def rectanglePerimeter(width, height):
       return ((width + height)*2)
    print(rectanglePerimeter(width, height))
except EOFError as e:
    print(end="")

width, height = map(int, input().split())
def rectanglePerimeter(width, height):
   return ((width + height)*2)
print(rectanglePerimeter(width, height))

Running it like this produces:

% echo "1 2" | test.py
6

---

I suspect IDLE is simply passing a single string to your script. The first input() is slurping the entire string. Notice what happens if you put some print statements in after the calls to input():

width = input()
print(width)
height = input()
print(height)

Running echo "1 2" | test.py produces

1 2
Traceback (most recent call last):
  File "/home/unutbu/pybin/test.py", line 5, in <module>
    height = input()
EOFError: EOF when reading a line

Notice the first print statement prints the entire string '1 2'. The second call to input() raises the EOFError (end-of-file error).

So a simple pipe such as the one I used only allows you to pass one string. Thus you can only call input() once. You must then process this string, split it on whitespace, and convert the string fragments to ints yourself. That is what

width, height = map(int, input().split())

does.

Note, there are other ways to pass input to your program. If you had run test.py in a terminal, then you could have typed 1 and 2 separately with no problem. Or, you could have written a program with pexpect to simulate a terminal, passing 1 and 2 programmatically. Or, you could use argparse to pass arguments on the command line, allowing you to call your program with

test.py 1 2