The sides of a triangle are labeled as (12x) feet, (10x + 3x squared minus 8) feet,...

1. Identify the sides of the triangle: The problem states the lengths of the three sides of the triangle are $(12x)$ feet, $(10x + 3x^2 - 8)$ feet, and $(15x + 4)$ feet.

1. Recall the formula for the perimeter of a triangle: The perimeter of any polygon is the sum of the lengths of its sides. For a triangle with sides $a$, $b$, and $c$, the perimeter $P$ is given by $P = a + b + c$.

3. Substitute the given side lengths into the perimeter formula:
$$P = (12x) + (10x + 3x^2 - 8) + (15x + 4)$$

4. Remove the parentheses and group like terms: To add the expressions, we remove the parentheses. Since we are adding, the signs of the terms inside the parentheses do not change.
$$P = 12x + 10x + 3x^2 - 8 + 15x + 4$$
Now, group the terms with the same power of $x$ together.
$$P = 3x^2 + (12x + 10x + 15x) + (-8 + 4)$$

5. Combine like terms: Add the coefficients of the $x$ terms and the constant terms.
For the $x$ terms: $12x + 10x + 15x = (12 + 10 + 15)x = 37x$
For the constant terms: $-8 + 4 = -4$

6. Write the final expression for the perimeter: Combine the simplified terms to get the perimeter.
$$P = 3x^2 + 37x - 4$$