Find x in a Parallelogram: Given Perimeter 36 and Side Length 15

To solve this problem, we'll follow these steps:

• Step 1: Use the perimeter formula for the parallelogram.
• Step 2: Substitute the known values and solve for $x$.

Now, let's work through each step:

Step 1: The formula for the perimeter of a parallelogram is given by:

$P = 2(a + b)$

where $a$ and $b$ are the lengths of the sides. In this case, we have:

$a = 15$ and $P = 36$.

Step 2: Substitute the values into the perimeter formula:

$36 = 2(15 + x)$

We can simplify this equation to solve for $x$:

$36 = 30 + 2x$

Step 3: Subtract $30$ from both sides:

$36 - 30 = 2x$

$6 = 2x$

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

$x = \frac{6}{2}$

$x = 3$

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