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

Given the parallelogram:

Calculate the perimeter of the parallelogram.

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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