Question

# If the lengths of the sides of a right angled triangle are in A.P., then show that their ratio is 3 : 4 : 5.

Let a - d, a, a + d, with d>0 be the lengths of sides of a right angled triangle.

∴  a + d, the largest side must be hypotenuse.
So, by pythagorus theorem
or
or                                    or         a = 4d

∴  Sides are 4d - d, 4d, 4d + d              or          3d, 4d, 5d
Hence, the sides are in the ratio 3:4:5.