The perimeter of a right-angled triangle is four times the shortest side. The ratio of the other two sides is

• 4 : 5
  
  Let the shortest (1st) side of a right-angled triangle=x, then perimeter=4x
  Therefore, sum of other two sides = 4x - x = 3x
  Let one of the other (2nd) side be a, then remaining (3rd) side will be (3x-a)
  According to Pythagoras theorem, x² + a² = (3x-a)²
  x² + a² = 9x² - 6ax + a²
  a = 4x/3
  Therefore, 3rd side=3x - a=3x - 4x/3=5x/3
  Hence required ratio = 2nd side : 3rd side = 4x/3 : 5x/3 = 4 : 5
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