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 3 inches wide on each side , the total area would have been ( m + 64 ) square inches . what is the perimeter of the photograph , in inches ?
Rationale: let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 6 ) ( y + 6 ) = m and so ( 2 ) xy + 6 x + 6 y + 36 = m + 64 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 x + 4 y + 32 = 64 2 x + 2 y = 16 , which is the perimeter of the photograph . the answer is a .
annotated_formula: divide(subtract(64, subtract(power(multiply(3, const_2), const_2), power(multiply(1, const_2), const_2))), const_2)