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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.
Calculate the length $t$ of the edge of piece $3$ and then calculate the lengths of all the other edges giving answers correct to $3$ significant figures. You can use the interactivity below to explore how the pieces fit together.
Can you find the sum of the squared sine values?
Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.