Parallelogram Perimeter: Express Total Length When One Side is 2X

Q: Why does the parallelogram have 4 sides if only 2 lengths are given?

In parallelograms, opposite sides are always equal! So if one side is X and another is 2X, then the opposite sides are also X and 2X respectively.

Q: How do I know which sides are opposite to each other?

Opposite sides are the ones that don't touch each other. In the diagram, sides AB and CD are opposite, and sides AC and BD are opposite.

Q: Is perimeter the same as circumference for parallelograms?

Yes! For polygons like parallelograms, perimeter and circumference mean the same thing - the total distance around the outside of the shape.

Perimeter Formula with Variable Side Lengths

A parallelogram has one side that is 2 times longer than the other. The length of the smaller side is X.

Express the circumference of the parallelogram in terms of X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's express the perimeter of the parallelogram using the variable X.

00:16 Remember: In a parallelogram, opposite sides are always equal.

00:22 Let's look at the longer sides first.

00:27 Based on the data, here's the length of one side.

00:33 Next, examine the given ratio of the sides.

00:40 Substitute this side value to calculate A B.

00:45 Remember: Opposite sides are equal in a parallelogram.

00:54 The perimeter is simply the total sum of all sides.

01:06 Now, plug in the correct values and solve to find the perimeter.

01:17 And that's how you find the solution to this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A parallelogram has one side that is 2 times longer than the other. The length of the smaller side is X.

Express the circumference of the parallelogram in terms of X.

Step-by-step solution

As is true of a parallelogram each pair of opposite sides are equal to one another

$AB=CD,AC=BD$

Given that $AB > AC$

Let's call AC by the name X and therefore:

$AB=2AC=2\times x=2x$

Now we know that:

$AB=CD=2x,AC=BD=x$

The perimeter is equal to the sum of all the sides together:

$2x+x+2x+x=6x$

Final Answer

4X+4

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are equal in length
Setup: If smaller side is X, then longer side equals 2X
Check: Perimeter = X + 2X + X + 2X = 6X total ✓

Common Mistakes

Avoid these frequent errors

Adding only two sides instead of all four
Don't calculate X + 2X = 3X and call it the perimeter! A perimeter needs ALL sides around the shape. Always add all four sides: X + 2X + X + 2X = 6X for the complete perimeter.

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 does the parallelogram have 4 sides if only 2 lengths are given?

In parallelograms, opposite sides are always equal! So if one side is X and another is 2X, then the opposite sides are also X and 2X respectively.

How do I know which sides are opposite to each other?

Opposite sides are the ones that don't touch each other. In the diagram, sides AB and CD are opposite, and sides AC and BD are opposite.

What if the problem said one side is 3 times longer instead of 2 times?

The method stays the same! If the smaller side is X and the longer side is 3X, then perimeter = $X + 3X + X + 3X = 8X$

Is perimeter the same as circumference for parallelograms?

Yes! For polygons like parallelograms, perimeter and circumference mean the same thing - the total distance around the outside of the shape.

Why is the answer 6X and not one of the given choices?

There seems to be an error in the explanation. Let me recalculate: if shorter side = X and longer side = 2X, then perimeter = $X + 2X + X + 2X = 6X$ . But this doesn't match the given options, so double-check the problem setup.

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