To find the perimeter of a triangle with given side lengths, you need to add all three sides together and combine any like terms. The side lengths given are:
1. [tex]\(8w + 8x\)[/tex] centimeters
2. [tex]\(3w + 10y\)[/tex] centimeters
3. [tex]\(4y + 8x\)[/tex] centimeters
Let's add these expressions step-by-step:
### Step 1: Write the full addition of the side lengths.
[tex]\[
(8w + 8x) + (3w + 10y) + (4y + 8x)
\][/tex]
### Step 2: Group the coefficients of each variable [tex]\(w\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex].
- For [tex]\(w\)[/tex]:
[tex]\[
8w + 3w = 11w
\][/tex]
- For [tex]\(x\)[/tex]:
[tex]\[
8x + 8x = 16x
\][/tex]
- For [tex]\(y\)[/tex]:
[tex]\[
10y + 4y = 14y
\][/tex]
### Step 3: Combine the grouped terms to form the perimeter expression.
Putting it all together, the expression for the perimeter of the triangle is:
[tex]\[
11w + 16x + 14y
\][/tex]
Therefore, the expression that represents the perimeter, in centimeters, of the triangle is:
[tex]\[
11w + 16x + 14y
\][/tex]
