Parallelogram Side Length: Finding Missing Side Given 12cm Perimeter

To solve this problem, follow these steps:

• Step 1: Identify the given information: one side $AB = 4 \, \text{cm}$, and the perimeter $P = 12 \, \text{cm}$.

• Step 2: Apply the perimeter formula for parallelograms, $P = 2a + 2b$.

• Step 3: Solve for the other side $b$.

Now, let's work through the calculations:

The formula for the perimeter of a parallelogram is:
$P = 2a + 2b$
Given $a = 4 \, \text{cm}$ and $P = 12 \, \text{cm}$, substituting these values gives:
$12 = 2(4) + 2b$
Simplifying, we have:
$12 = 8 + 2b$
Subtract 8 from both sides:
$4 = 2b$
Divide both sides by 2 to find $b$:
$b = 2$

Therefore, the length of the other side is $2 \, \text{cm}$.