Perimeter of a Parallelogram: Using the properties of the perimeter of the parallelogram

To find the perimeter of parallelogram ABCD, we begin by identifying the lengths of its sides:

• Side AB is given as $10$ cm.
• Side BC is given as $8$ cm.

In a parallelogram, opposite sides are equal in length. Therefore, we also know:

• Side CD is $10$ cm (since it is opposite to AB).
• Side DA is $8$ cm (since it is opposite to BC).

The formula for the perimeter $P$ of a parallelogram is:

$P = 2 \times (\text{length}_1 + \text{length}_2)$

Substituting the known values into the formula, we have:

$P = 2 \times (10 + 8)$

$P = 2 \times 18$

$P = 36 \, \text{cm}$

Thus, the perimeter of parallelogram ABCD is $36$ cm.

The correct answer is $\textbf{36 cm}$, which corresponds to choice 3.

To solve this problem, follow these steps:

• Step 1: Understand the properties of a parallelogram.
• Step 2: Apply the perimeter formula for a parallelogram.
• Step 3: Compute the value using the given side lengths.

Now, let's calculate:

Step 1: In a parallelogram, opposite sides are of equal length. Here, $AB = CD = 15 \, \text{cm}$ and $BC = DA = 10 \, \text{cm}$.

Step 2: The perimeter $P$ of a parallelogram is calculated using the formula:

$P = 2(a + b)$

where $a$ and $b$ are the lengths of two adjacent sides.

Step 3: Substituting the given values for $a$ and $b$:

$P = 2(15 + 10) = 2 \times 25 = 50 \, \text{cm}$

Therefore, the perimeter of parallelogram ABCD is 50 cm.

Among the choices, option 1: 50 cm is the correct answer.

To solve the problem of finding the perimeter of the parallelogram ABCD, we must first ensure we have complete information. The perimeter $P$ of a parallelogram is calculated using the formula:

$P = 2(a + b)$

where $a$ and $b$ are the lengths of two adjacent sides.

Upon analyzing the problem, we find:

• The visual suggests only one side length is explicitly labeled as 7.
• For calculating the full perimeter, both adjacent side lengths are needed.

In the absence of additional side length information or any angles, we cannot accurately determine the perimeter of this specific parallelogram.

Considering the facts, there is not enough data to compute the perimeter.

Therefore, the correct choice is: Not enough data.