The triangle below has angles $\lambda ,2\lambda$ and $7\lambda$ where $\lambda \in \mathbb{N}$ is a fixed constant.

1. Find the value of $\lambda$.

2. Given that the perimeter of the triangle is $72\text{cm}$, find the length of $x$, giving your answer in the form

The angles in a triangle sum to ${180}^{\circ }$

Let the shortest side be $y$ and the longest side $z$.

Use the sine rule to express $y$ and $z$ in terms of $x$.

The perimeter is $x+y+z$.