In a right triangle, the hypotenuse is 1 meter more than the length of one of the legs and this leg is 17 meters more than the length of the shortest leg. What are the lengths of the three sides of the triangle?

let x - shortest leg

   y - longer leg 

 z -hypotenuse

z = y+1

x = y-17

y = x + 17

z = x + 18

z^2 = x^2 + y ^2

z^2 = x^2 + 324

y^2 = 324

y =18

z = 19

x =1