Let ABC is the right angle triangle, right angle at B

So, ∠B = 90 degree

Let the length of the hypotenuse AC = x

Now, base BC = x - 1

and altitude AB = x - 18

Now, according to Pythagoras Theorem,

     AC² = AB² + BC²

=> x² = (x - 18)² + (x - 1)²

=> x² = x² + (18)^{2 -} 2*x*18 + x² + 1^{2 -} 2*x*1

=> x² = x² + 324 - 36x + x² + 1 - 2x

=> x² - x² = 324 - 36x + x² + 1 - 2x

=> 0 = 324 - 36x + x² + 1 - 2x

=> x² - 38x + 325 = 0

=> x² - 25x - 13x + 325 = 0

=> x(x - 25) - 13(x - 25) = 0

=> (x - 25)*(x - 13) = 0

=> x = 13, 25

Since x = 13 is not possible.

So, x = 25

Now, AC = 25 cm

BC = 25 - 1 = 24 cm

and AC = 25 - 18 = 7 cm

So, the length of sides of triangle are: 25 cm, 24 cm, 7 cm