13. The diagram shows a triangle joined to a square to form an irregular pentagon. The triangle has the same perimeter as the square.
What is the ratio of the perimeter of the pentagon to the perimeter of the square?
A 2:1
B $3: 2$
C 4:3
D 5:4
E 6: 5
13. B Let the length of the edge of the square be 1 unit. Therefore the perimeter of the square and hence the perimeter of the triangle is 4 units. Since the pentagon is made by joining the square and the triangle along one common edge, the perimeter of the pentagon is equal to the sum of their perimeters minus twice the length of the common edge or $(4+4-2)$ units $=6$ units. Therefore the ratio of the perimeter of the pentagon to the perimeter of the square is $6: 4=3: 2$.