about to only mathematics

Options

A. 16
B. 18
C. 24
D. 22

Answer

B, D

Explanation

Whenever cosine of angle and sides are given or to find out, we should always use Cosine law.
i.e., `cos A=(b^(2)+c^(2)-a^(2))/(2bc),cosB=(a^(2)+c^(2)-b^(2))/(2ac)`
and `cos C=(a^(2)+b^(2)-c^(2))/(2ab)`

`:. cos P=(b^(2)+c^(2)-a^(2))/(2bc)`
`(1)/(3)=((2n-4)^(2)+(2n+2)^(2)-(2n+6)^(2))/(2(2n+4)(2n+2)) [:. cos p=(1)/(3)"given"]`
`rArr (4n^(2)-16)/(8(n+1)(n+2))=(1)/(3)`
`rArr (n^(2)-4)/(2(n+1)(n+2))=(1)/(3)`
`rArr ((n-2))/(2(n+1))=(1)/(3)`
`rArr 3n-6=-2n+2rArr n=8`
`:.` Sides are `(2n+2),(2n+4),(2n+6),i.e.,18,20,22`