Pythagoras mod 5

Prove that for every right angled triangle which has sides with integer lengths: (1) the area of the triangle is even and (2) the length of one of the sides is divisible by 5.
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Problem

Prove that for every right angled triangle which has sides with integer lengths:

  1. the area of the triangle is even and
  2. the length of one of the sides is divisible by 5.