17. Rectangle $W X Y Z$ is cut into four smaller rectangles as shown. The lengths of the perimeters of three of the smaller rectangles are 11, 16 and 19. The length of the perimeter of the fourth smaller rectangle lies between 11 and 19. What is the length of the perimeter of $W X Y Z$ ?
A 28
B 30
C 32
D 38
E 40
Solution
B

From the diagram, we see that the sum of the perimeters of two diagonally opposite smaller rectangles is equal to the perimeter of the large rectangle. We are told that the rectangle whose perimeter we do not know has neither the largest nor the smallest of the perimeters of the smaller rectangles. Hence the rectangles with perimeters 11 and 19 are the ones with the largest and smallest perimeters respectively and so are two diagonally opposite rectangles. Therefore the perimeter of the large rectangle is $19+11=30$.