The sides can be represented by a-d, a, a+d where a+d = the hypotenuse = 15 cm

So the first equation comes from that:

a+d = 15

The second equation comes from the Pythagorean theorem:

(a-d)² + a² = (a+d)²

         a² = (a+d)² - (a-d)²

         a² = [(a+d)-(a-d)][(a+d)+(a-d)]
        
         a² = [a+d-a+d][a+d+a-d]

         a² = [2d][2a]

         a² = 4ad

   a² - 4ad = 0

  a(a - 4d) = 0

a = 0;  a - 4d = 0

             a = 4d 

For a = 0,               
not possible because
sides of a triangle are
positive numbers.        For a = 4d

                           a+d = 15
  
                          4d+d = 15 

                            5d = 15

                             d = 3
                           
                             a = 4(3)

                             a = 12

The sides are 

a-d = 12-3 = 9
  a = 12
a+d = 12+3 = 15 (given)    9, 12, 15

Edwin