Can you re-arrange the pieces of the puzzle to form a rectangle by sliding the pieces without rotating them? Now can you re-arrange the pieces to form an equilateral triangle by flipping the pieces numbered 2 and 5 and moving them into new positions?

You can assume that pieces 1 and 5 each have a side of length one unit, that the pieces as shown form a perfect square of area one square unit and that they do fit together to form a perfect equilateral triangle of the same area. This is will tell you that some of the angles are 60 ^o, some are 30 ^o and some are 90 ^o.

First calculate the length of the edge of piece 3 which is labelled 't' and then calculate the lengths of all the other edges giving answers correct to 3 significant figures.