Solve for X: Parallelogram with Perimeter 42 and Side Length x+1

To solve this problem, we'll follow these steps to find $x$:

• Step 1: Use the formula for the perimeter of a parallelogram.
• Step 2: Set up an equation involving $x$ and solve for $x$.
• Step 3: Substitute the values and perform calculations to find $x$.

Let's proceed:

Step 1: The formula for the perimeter of a parallelogram is:
$P = 2(a + b)$ where $a$ and $b$ are the lengths of two adjacent sides. Here, $a = x$ and $b = x+1$.

Step 2: According to the problem, the perimeter $P = 42$. Therefore, we set up the equation:
$42 = 2(x + (x + 1))$

Step 3: Simplify and solve for $x$:
$42 = 2(2x + 1)$
$42 = 4x + 2$
Subtract 2 from both sides:
$40 = 4x$
Solve for $x$ by dividing both sides by 4:
$x = 10$

Therefore, the solution to the problem is $x = 10$.