To find the perimeter of a triangle, you need to sum the lengths of all its sides.
The given side lengths of the triangle are:
- [tex]\( -8a \)[/tex]
- [tex]\( a + 4 \)[/tex]
- [tex]\( 12a + 10 \)[/tex]
Step-by-Step Solution:
1. Identify the side lengths:
- First side length: [tex]\( -8a \)[/tex]
- Second side length: [tex]\( a + 4 \)[/tex]
- Third side length: [tex]\( 12a + 10 \)[/tex]
2. Sum up all the side lengths:
[tex]\[
\text{Perimeter} = (-8a) + (a + 4) + (12a + 10)
\][/tex]
3. Combine like terms:
- Combine the [tex]\(a\)[/tex] terms: [tex]\( -8a + a + 12a = (-8 + 1 + 12)a = 5a \)[/tex]
- Combine the constants: [tex]\(4 + 10 = 14\)[/tex]
4. Simplify the expression:
[tex]\[
\text{Perimeter} = 5a + 14
\][/tex]
Thus, the perimeter of the triangle is given by the expression [tex]\( 5a + 14 \)[/tex].
Given that the numerical result provided is:
[tex]\[
18
\][/tex]
This implies that if we substitute the correct value of [tex]\( a \)[/tex], the expression [tex]\(5a + 14\)[/tex] yields [tex]\(18\)[/tex].
