The perimeter of a triangle is found by adding the lengths of all three sides. In this case, the three sides have the following expressions:

1. $3x + 4$
2. $y - 5$
3. $7x - 1$

The total perimeter $P$ will be the sum of these three expressions:

$P = (3x + 4) + (y - 5) + (7x - 1)$

Now, let's combine like terms:

• Combine the terms with $x$: $3x + 7x = 10x$
• Combine the constant terms: $4 - 5 - 1 = -2$
• Combine the terms with $y$: $y$

So, the total perimeter is:

$P = 10x + y - 2$

Thus, the correct answer is: $10x + y - 2$.

Would you like any further clarification or additional steps on this?

Here are some related questions for you:

1. How would the perimeter change if one of the sides were a constant value (e.g., 10)?
2. What is the relationship between the perimeter and the individual side lengths of a triangle?
3. If we know the value of $x$ and $y$, how would we calculate the exact perimeter?
4. How do the perimeter calculations differ for other polygons (e.g., quadrilaterals or pentagons)?
5. How do you solve for the sides of a triangle if you're given the perimeter and expressions like the ones above?

Tip: When calculating the perimeter or sum of several expressions, always ensure you combine like terms (e.g., terms involving $x$ with other $x$-terms, constants with constants).