A pentagon has three sides with length x, and two sides with the length 3x. If x is `2/3` of an inch, what is the perimeter of the pentagon?

Answer

To find the perimeter of the pentagon, we will follow these steps:

### Step 1: Identify the lengths of the sides
The pentagon has three sides of length \( x \) and two sides of length \( 3x \).

### Step 2: Substitute the value of \( x \)
We know that \( x = \frac{2}{3} \) inches. Therefore, we can substitute \( x \) into the lengths of the sides:
- Length of three sides: \( 3 \times x = 3 \times \frac{2}{3} = 2 \) inches
- Length of two sides: \( 2 \times 3x = 2 \times 3 \times \frac{2}{3} = 4 \) inches

### Step 3: Calculate the total length of the sides
Now, we can calculate the total length of all sides:
- Total length from three sides: \( 3 \times x = 3 \times \frac{2}{3} = 2 \) inches
- Total length from two sides: \( 2 \times 3x = 2 \times 2 = 4 \) inches

### Step 4: Find the perimeter
The perimeter \( P \) of the pentagon is the sum of the lengths of all its sides:
\[ P = (3 \times x) + (2 \times 3x) = 2 + 4 = 6 \text{ inches} \]

### Final Answer
The perimeter of the pentagon is \( 6 \) inches.

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