Write and simplify an expression to represent the perimeter of the triangle. You m

Question

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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:

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