Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 108 ) square inches . what is the perimeter of the photograph , in inches ?
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 8 ) ( b + 8 ) = m + 108 - - - - - - - - - > ( l + 8 ) ( b + 8 ) - 108 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 8 ) ( b + 8 ) - 108 lb + 2 l + 2 b + 4 = lb + 8 l + 8 b + 64 - 108 simplify 6 l + 6 b = 48 - - - - - - > 2 ( l + b ) = 16 ( check eq ( 1 ) ) answer is c"
annotated_formula: divide(subtract(108, subtract(power(multiply(4, const_2), const_2), power(multiply(1, const_2), const_2))), const_2)