when shapes are similar their areas are in proportion to the squares of corresponding sides
drop a perpendicular from the apex at the right angle to form two similar triangles (relatively straightforward to justify) which are similar to the original triangle
k(5^2) = k(4^2) + k(3^2)
and this generalises...
not that helpful as a means of justifying the theorem maybe, but a neat enough way of tying in the area property of similar shapes
[ from the website betterexplained ]
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