Find X in Rectangle: Perimeter 32 with Side Length 2x

To solve this problem, let's clearly follow these steps:

• Step 1: Identify the information given and needed for solving.

• Step 2: Apply the perimeter formula for a rectangle.

• Step 3: Solve for the unknown variable $x$.

Step 1: The rectangle has a perimeter $P = 32$. One pair of opposite sides is $2x$ and the other pair is 10.

Step 2: The perimeter of a rectangle is calculated by
$P = 2(l + w)$ where $l$ is the length and $w$ is the width.
Here, $l = 2x$ and $w = 10$.

Step 3: Substitute the given values into the formula:

$32 = 2(2x + 10)$

Expand the equation:

$32 = 4x + 20$

To solve for $x$, subtract 20 from both sides:

$32 - 20 = 4x$

$12 = 4x$

Finally, divide both sides by 4 to find $x$:

$x = \frac{12}{4}$

$x = 3$

Therefore, the solution to the problem is $x = 3$.