If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.  Choose the correct answer.
A) 40 cm B) 45 cm C) 50 cm D) 52 cm E) 57 cm

Rationale: explanation : let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( 1 ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( 2 ) solving 1 & 2 , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : option c
Answer: C