Problem Solving with Triangle Ratios

Consider a triangle ABC where the lengths of sides AB, BC, and CA are represented by the variables $a$, $b$, and $c$, respectively. If the perimeter of triangle ABC is 40 units and the following ratios hold true: $AB:BC = 3:5$ and $BC:CA = 5:7$, what is the length of side CA?

Let the lengths be expressed in terms of ratios. First, let $AB = 3x$, $BC = 5x$, and $CA = 7y$. Since $BC = 5x$ and $CA = 7y$, we can also express $y$ in terms of $x$. Use the given perimeter condition to find the value of $x$.