The perimeter of a rectangular painting is 332 centimeters. if the length of the painting is 92 centimeters, what is its width?

  The width of the rectangular painting is:  " 74 cm " .

Explanation:

P = 2L + 2w ;

in which:  P = perimeter = 332 cm (given) ;
                L = length = 92 cm (given) ;
                w = width = ? (to be solved) ;

First,  given:  P = 2L + 2w ;

Subtract "2L" from EACH SIDE of the equation ;
   to isolate "2w" on one side of the equation ;

    P − 2L = 2L + 2w − 2L  ;

to get:   P − 2L = 2w ;

↔  2w = P − 2L ;

Now:

Plug in our given values into the equation / formula ; and solve for "w" ;

2w =  332 − 2(92) ;

2w =  332 − 184  ;

2w =  148 ;

Now, divide EACH SIDE of the equation by "2" ;
   to isolate "w" on one side of the equation ; and to solve for "w" ;

    2w / 2 = 148 / 2 ;

           w = 74 cm .