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The hard part of this is doing the trigonometry to determine the length of the fold, once that’s worked out it’s pretty obvious how long it is. And once I’d done the trigonometry it became apparent that there is a much easier way to find the length of the fold involving congruent triangles.

Nevertheless, here’s some code to check the answer (and it uses my new

`printf()`

function (from theenigma.pylibrary) that interpolates variables into the print format string without you having to specify them as arguments).Solution:The fold is 10cm long.The area of the square is 80 cm².

Here’s the diagram I used to determine the length of the fold:

Consider the square ABCD, of side

2l.(That’s the letterl).The fold places A on E (the midpoint of CD), which makes ADE a right-angled triangle with hypotenuse

l√5,and angle at A ofθ.The fold line itself is the perpendicular bisector of AE, labelled FG.

But the right-angled triangle FGH is congruent to ADE, with length FH being

2land angle at F beingθ.Hence the length along the fold FG is also

l√5.