Parallelogram Perimeter: Express in Terms of X When One Side is Double Another

To solve this problem, we need to calculate the perimeter of the parallelogram using given information. Here are the steps to find the solution:

• Step 1: Identify the Longest Side.
  The longest side of the parallelogram, denoted by $X$, is given as $a$. Therefore, $a = X$.
• Step 2: Determine the Other Side Length.
  Given $a > 2b$, typically $X = 2b$ as a common interpretation for solving problems.
  Thus, the other side $b$ is half the longer side: $b = \frac{X}{2}$.
• Step 3: Apply the Perimeter Formula.
  The perimeter $P$ of a parallelogram is calculated as $P = 2(a + b)$.
  Plug in the values: $a = X$, $b = \frac{X}{2}$.
  Thus, perimeter $P = 2\left(X + \frac{X}{2}\right) = 2\left(\frac{2X}{2} + \frac{X}{2}\right) = 2\left(\frac{3X}{2}\right) = 3X$.

Therefore, the perimeter of the parallelogram in terms of $X$ is $\mathbf{3X}$.