In a ∆ PQR , P is the largest angle and cosP = (1)/(3) . Further...

Consider the following figure:

We assumed the value of sides in terms of $n$, which satisfies our given condition.

Now applying cosine rule,

$cosP = \dfrac{{\left(2n + 2\right)}^{2} + {\left(2n + 4\right)}^{2} - {\left(2n + 6\right)}^{2}}{2\left(2n + 2\right)\left(2n + 4\right)}$

$\text{=}\dfrac{4{n}^{2} - 16}{8\left(n + 1\right)\left(n + 2\right)} = \dfrac{1}{3}$

$\text{=}\dfrac{{n}^{2} - 4}{2\left(n + 1\right)\left(n + 2\right)} = \dfrac{1}{3}$

$⇒ \dfrac{n - 2}{2\left(n + 1\right)} = \dfrac{1}{3}$

$⇒ 3n - 6 = 2n + 2 ⇒ n = 8$

Length of the sides will be $18, 20$and $22$.