If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of length of the sides of this triangle is:

Correct option is C. 4 : 5: 6
a < b < c are in A.P.∠ C = 2∠ A (Given)⇒sin C = sin 2A⇒sin C = 2sin A. cos A

sin C
--- = 2cos A
sin A
⇒ca = 2 b

2bc

b^2 + c^2 - a^2
Put a = b - λ, c = b + λ, λ > 0⇒λ = b
5⇒ a = b - b
5 = 4b
5, c = b + b
5 = 6b
5⇒ required ratio = 4 : 5 : 6