To find the total perimeter of the triangle with sides [tex]\(3x + 4\)[/tex], [tex]\(y - 5\)[/tex], and [tex]\(7x - 1\)[/tex], we need to add up the lengths of all three sides.
1. Write down the expressions for each side:
- First side: [tex]\(3x + 4\)[/tex]
- Second side: [tex]\(y - 5\)[/tex]
- Third side: [tex]\(7x - 1\)[/tex]
2. Sum the expressions to find the perimeter:
[tex]\[
\text{Perimeter} = (3x + 4) + (y - 5) + (7x - 1)
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(3x + 7x = 10x\)[/tex]
- Combine the constant terms: [tex]\(4 - 5 - 1 = -2\)[/tex]
So, we have:
[tex]\[
\text{Perimeter} = 10x + y - 2
\][/tex]
So the total perimeter of the triangle is [tex]\(\boxed{10x + y - 2}\)[/tex].
