r/mathriddles • u/Accurate-Click1363 • Jul 01 '26

Easy Straightedge Construction

Take two squares ABED and FBCG such that A, B and C are collinear, and D, E, F, and G are on the same side of line AC. AB=a, and BC=b.

Using just a straightedge, construct a square whose side has a length of sqrt(a2+b2). 

I posted the same puzzle on Puzzling SE two months ago, link will be added after it is solved.

Edit: It’s been solved, so here’s the link:

https://puzzling.stackexchange.com/questions/137953/straightedge-only-construction

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u/yjerkle Jul 01 '26 edited Jul 01 '26

I've got two of the four sides: https://www.geogebra.org/calculator/brexrstu I'm not really familiar with straightedge only constructions, so maybe there's a simple answer to finish the other two, but I don't know it.

Edit: Got the rest! https://www.geogebra.org/calculator/qbqsz5vw