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 + 52) square inches. What is the perimeter of the photograph, in inches? Select the correct option.
A) 10 B) 36 C) 38 D) 40 E) 42

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 + 6 ) ( b + 6 ) = m + 52 - - - - - - - - - > ( l + 6 ) ( b + 6 ) - 52 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 6 ) ( b + 6 ) - 52 lb + 2 l + 2 b + 4 = lb + 6 l + 6 b + 36 - 52 simplify 4 l + 4 b = 20 - - - - - - > 2 ( l + b ) = 10 ( check eq ( 1 ) ) answer is a"
Answer: A