Solve for X: Parallelogram with Perimeter 20 and Side Ratio 1:3

To calculate $x$ in the given parallelogram, we begin by noting the given perimeter formula for the parallelogram, $P = 2(a + b)$.

The two sides, as given, are $a = x$ and $b = 3x$. Substituting these into the formula gives:

$P = 2(x + 3x)$

We know the perimeter $P = 20$, therefore:

$2(x + 3x) = 20$

Simplifying inside the parentheses, $x + 3x = 4x$, we rewrite the equation as:

$2 \times 4x = 20$

Which gives:

$8x = 20$

To solve for $x$, divide both sides by 8:

$x = \frac{20}{8}$

Simplifying gives:

$x = \frac{5}{2}$

Or, $x = 2.5$.

Thus, the value of $x$ is $\boxed{2\frac{1}{2}}$.