Triangular conundrum

Question

Place any three numbers on the vertices of a triangle:

         5
        / \
       /   \
      /     \
     8-------4

Calculate their differences, going one way:

         5
        / \
   -3  /   \ -1
      /     \
     8-------4
         4

Place another number inside the triangle:

         5
        / \
   -3  /   \ -1
      / 15  \
     8-------4
         4

Add the centre number to a vertex, and multiply the total by the opposite edge. Do this for each vertex. Add them together.

$(15+5)\times4=80$
$(15+8)\times-1=-23$
$(15+4)\times-3=-57$

$80-23-57=0$

You got $0$. Why?

$\begingroup$ Because math is cool. $\endgroup$
– Daniel Mathias
Apr 7, 2020 at 11:41 — Daniel Mathias, Apr 7, 2020 at 11:41

newbie · Accepted Answer · 2020-04-07 11:48:07Z

7

Although weird-looking in hindsight, some elementary maths clearly show why.

answered Apr 7, 2020 at 10:36

newbie

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$\begingroup$ Should be $(d+c)(a-b)$ et cetera $\endgroup$
– Daniel Mathias
Apr 7, 2020 at 11:45
$\begingroup$ Sorry, totally forgot about that when I started copying that formula :( Fixed, thanks! @DanielMathias $\endgroup$
– newbie
Apr 7, 2020 at 11:48

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