if the angles of a right angled triangle are in A.P, then ratio of its sides

Let the sides of the right triangle be, a - d , a and a+ d

now, (a + d)2 = (a - d)2 + a2  [Pythagoras theorem]

 so, a2 + d2 + 2ad = a2 + d2 - 2ad + a2

 ⇒ 4ad = a2

 ⇒ a = 4d

so the sides of triangle are : 3d, 4d and 5d  [on substituting the value of a]

Hence the sides of the right triangle are in the ratio  of 3 : 4 : 5