Find Side Length AC in Parallelogram: Using Perimeter = 20 and AB = 5

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

• Step 1: Use the formula for the perimeter of a parallelogram.
• Step 2: Set up the equation using the given information.
• Step 3: Solve for $X$ and find the length of AC.

Now, let's work through each step:
Step 1: Recall that the perimeter of a parallelogram is given by the formula $P = 2(a + b)$, where $a$ and $b$ are the lengths of adjacent sides.
Step 2: In our parallelogram, opposite sides are equal. Therefore, the perimeter formula can be expressed as: $P = 2(AB + AC) = 20$ Substituting the given lengths: $2(5 + 2X) = 20$
Step 3: Simplify the equation: $2 \times (5 + 2X) = 20 \\ 10 + 4X = 20 \\ 4X = 10 \\ X = 2.5$ Now, substitute back to find the length of side AC: $AC = 2X = 2 \times 2.5 = 5$

Therefore, the length of side AC is $\bold{5}$.

The correct choice from the given options is $\bold{3}$: $\bold{5}$.