Rectangle Perimeter Problem: Solving for X When One Side is 2x

To solve this problem, we will determine $x$ using the perimeter formula for a rectangle. The steps are as follows:

• Step 1: Set up the perimeter equation for this problem using the formula $P = 2(l + w)$.
• Step 2: Identify the given dimensions: $l = 2x$ and $w = x$.
• Step 3: Substitute these dimensions into the perimeter equation: $2(2x + x) = 12$.
• Step 4: Simplify the equation to solve for $x$.

Now, let's follow these steps:

Step 1: The perimeter $P = 12$ units. Thus, we use the equation:

$2(l + w) = 12$

Step 2: Substitute the known values of length and width:

$2(2x + x) = 12$

Step 3: Simplify the equation inside the parentheses:

$2(3x) = 12$

Step 4: Divide both sides by 2 to solve for $x$:

$3x = 6$

Finally, divide by 3:

$x = 2$

Therefore, the solution to the problem is $x = 2$.