Find Side CD in a Parallelogram: Given AB = 15cm and Perimeter = 40cm

To solve this problem, we'll identify the values and apply the perimeter formula specific to parallelograms.

• Step 1: Identify the given values.
• Step 2: Apply the perimeter formula for a parallelogram.
• Step 3: Solve for the unknown side.

Now, let's work through each step:

Step 1: We know $AB = 15$ cm and the perimeter of the parallelogram is 40 cm. Assume $CD = x$ cm (since in a parallelogram opposite sides are equal, $CD = DA$ and $AB = BC$).

Step 2: The formula for the perimeter of a parallelogram is $2(a + b)$, where $a$ and $b$ are the lengths of any two adjacent sides.

Step 3: Plugging in the known values, we have $2(15 + x) = 40$.

Simplify and solve for $x$:

$30 + 2x = 40$

$2x = 40 - 30$

$2x = 10$

$x = \frac{10}{2} = 5$

Therefore, the solution to the problem is $\text{side } CD = 5 \text{ cm}$.

Checking the multiple-choice answers, option 4 matches our solution:

$5$.