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Michael and Robert from Necton Middle School in Norfolk sent the following solution, where the sides all add up to 17:
Simone from Stroud Green Primary School sent us another solution where the sides all add up to 17.
In fact, there are lots more solutions. Here's a list of them (including the two shown above). Each group of four numbers makes up a side of the triangle. Of course, within a side you can switch round numbers that aren't on a corner, but that doesn't really give any new solutions.