Solve for X: Parallelogram with Perimeter 30 and Side Length 8

The problem involves finding the value of $X$ in a parallelogram with sides given and a specified perimeter. We will use the formula for the perimeter of a parallelogram.

The formula for the perimeter $P$ of a parallelogram is:

$P = 2(a + b)$

Given that:

• One side $AB = a = 8$.
• The other side $AC = b = X + 2$.
• The perimeter $P = 30$.

Substitute the given values into the perimeter formula:

$2(8 + (X + 2)) = 30$

Simplify the expression inside the parentheses:

$8 + X + 2 = X + 10$

Now the equation becomes:

$2(X + 10) = 30$

Divide both sides by 2:

$X + 10 = 15$

Subtract 10 from both sides to solve for $X$:

$X = 15 - 10$

Thus:

$X = 5$

The value of $X$ is therefore $\textbf{5}$.