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In this answer, the writer presents a beautiful proof of Heron's formula.

Image (Source: the same answer)

The identity written $x+y+z=xyz$, which he proved by the use of similar triangles and some algebra.

How can I explain this intuitively to someone who doesn't know similar triangles? And/or is there some intuition behind this formula that makes it look easy to observe how this comes?

ultralegend5385
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    Related: "Heron's Formula Intuitive Geometric Proof". The question itself gives a visual demonstration of the relation $x+y+z=xyz$, taken from this page (via uga.edu), although similar triangles are involved. (Avoiding similarity altogether is a pretty big ask.) – Blue Aug 20 '21 at 10:36
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    @Blue: That proof helped a lot and in my opinion, I think I will be able to explain that to the students (I'm just a schooler, but I like to teach maths to my juniors), and there is even no algebra there, so it's very intuitive. Thanks a lot :D, although I think I might put this open, who knows someone might be able to explain it ;) – ultralegend5385 Aug 21 '21 at 00:29

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