PS Archive | Re: 45-45-90 triangles and their side ratio

Below PS question is from the officialguide.



Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?

(A) 2:3
(B)\sqrt{2} :2
(C) 2\sqrt{2} :3
(D) 1:1
(E)\sqrt{2}:1

Figures X and Y are attached to this post.
Answer given in official guide -C

Now figure X is a square and it can be derived that the two triangles are isosceles