Question

Write and simplify an expression to represent the perimeter of the triangle. You m
ust show ALL work to earn full credit.

Note: it is not drawn to scale.

Triangle side 1: 2x-1
Triangle side 2: 3x
triangle side 3: 5(2x-1)

Answer 1

To find the perimeter of the triangle, we need to sum the lengths of all three sides. The sides of the triangle are:

1. Side 1: \( 2x - 1 \)
2. Side 2: \( 3x \)
3. Side 3: \( 5(2x - 1) \)

### Step 1: Write the expression for the perimeter

The perimeter \( P \) of the triangle can be expressed as:

\[
P = \text{Side 1} + \text{Side 2} + \text{Side 3}
\]

Substituting the expressions for the sides, we have:

\[
P = (2x - 1) + (3x) + (5(2x - 1))
\]

### Step 2: Expand the expression for Side 3

Now we will expand \( 5(2x - 1) \):

\[
5(2x - 1) = 5 \cdot 2x - 5 \cdot 1 = 10x - 5
\]

### Step 3: Substitute the expanded expression back into the perimeter equation

Now, substitute \( 10x - 5 \) back into the perimeter equation:

\[
P = (2x - 1) + (3x) + (10x - 5)
\]

### Step 4: Combine like terms

Next, we need to combine all the \( x \) terms and the constant terms:

- Combine \( 2x \), \( 3x \), and \( 10x \):
\[
2x + 3x + 10x = 15x
\]

- Combine the constant terms \(-1\) and \(-5\):
\[
-1 - 5 = -6
\]

### Step 5: Write the simplified expression for the perimeter

Putting it all together, the expression for the perimeter is:

\[
P = 15x - 6
\]

### Final Answer

The simplified expression for the perimeter of the triangle is:

\[
\boxed{15x - 6}
\]