I think proof #6 on this page is easier to follow and uses the same similar triangles. But then it’s just some basic algebra without assuming anything about are

I think proof #6 on this page is easier to follow and uses the same similar triangles. But then it’s just some basic algebra without assuming anything about areas of similar triangles :) https://www.cut-the-knot.org/pythagoras/index.shtml#6 https://www.cut-the-knot.org/pythagoras/index.shtml#6