Calculate the Perimeter of Parallelogram ABCD with Side Length 10

Q: Why don't I need to know what X equals?

The problem asks for the perimeter in terms of X, not a numerical value. Your answer $ 2X + 20 $ is complete because it shows the relationship between X and the perimeter.

Q: How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in a parallelogram. So AB = CD (both equal X) and AD = BC (both equal 10). This is a key property!

Q: Can I use P = 4s like for a square?

No! The formula P = 4s only works for squares where all sides are equal. For parallelograms with different side lengths, always use P = 2(base + side).

Q: What if the diagram shows different measurements?

Always use the given measurements from the problem. In this case, one side is X and the adjacent side is 10, so the formula becomes $ P = 2(X + 10) $.

Q: Do I need to simplify 2(X + 10)?

Yes! Always distribute to get the final answer: $ 2(X + 10) = 2X + 20 $. This matches the answer choices and is the standard form.

Parallelogram Perimeter with Variable Side Lengths

Calculate the perimeter of the parallelogram ABCD.

AB is parallel to CD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the parallelogram

00:03 The perimeter of the parallelogram equals the sum of the sides

00:07 Opposite sides are equal in a parallelogram, so we'll multiply the sum

00:09 We'll substitute appropriate values according to the given data, and solve for the perimeter

00:16 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the perimeter of the parallelogram ABCD.

AB is parallel to CD.

Step-by-step solution

To find the perimeter of the parallelogram ABCD, we will use the formula for the perimeter of a parallelogram:

The formula for the perimeter $P$ is $P = 2 \times (\text{length of one base} + \text{length of one side})$ .

Given that:

The length of the base (either AB or CD) is $X$ .
The length of the side (either AD or BC) is 10.

Substituting these values into the formula for the perimeter, we get:

P = 2 \times (X + 10)

Distribute the 2:

P = 2X + 20

Therefore, the perimeter of parallelogram ABCD is $2X + 20$ .

The correct answer, as per the choices given, is choice 4: $2x+20$ .

Final Answer

$2x+20$

Key Points to Remember

Essential concepts to master this topic

Formula: Parallelogram perimeter equals 2 times sum of adjacent sides
Technique: P = 2(X + 10) = 2X + 20 using distributive property
Check: Opposite sides are equal: AB = CD = X, AD = BC = 10 ✓

Common Mistakes

Avoid these frequent errors

Adding all four individual side lengths
Don't calculate X + 10 + X + 10 = 2X + 20 by adding each side separately! This takes longer and leads to arithmetic errors. Always use the perimeter formula P = 2(base + side) to work more efficiently.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the parallelogram using the data below.

FAQ

Everything you need to know about this question

Why don't I need to know what X equals?

The problem asks for the perimeter in terms of X, not a numerical value. Your answer $2X + 20$ is complete because it shows the relationship between X and the perimeter.

How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in a parallelogram. So AB = CD (both equal X) and AD = BC (both equal 10). This is a key property!

Can I use P = 4s like for a square?

No! The formula P = 4s only works for squares where all sides are equal. For parallelograms with different side lengths, always use P = 2(base + side).

What if the diagram shows different measurements?

Always use the given measurements from the problem. In this case, one side is X and the adjacent side is 10, so the formula becomes $P = 2(X + 10)$ .

Do I need to simplify 2(X + 10)?

Yes! Always distribute to get the final answer: $2(X + 10) = 2X + 20$ . This matches the answer choices and is the standard form.

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