Parallelogram Perimeter Problem: Solving for X when Perimeter is 80 cm

Q: Why do I multiply by 2 for each side length?

A parallelogram has four sides, but opposite sides are equal. So if one side is x, there are two sides with length x. If another side is 2x, there are two sides with length 2x. That's why the perimeter is 2x + 2(2x).

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

In parallelogram ABCD, AB and CD are opposite (both labeled x), and BC and AD are opposite (both labeled 2x). Opposite sides are the ones that don't share a vertex.

Q: Can I leave my answer as a mixed number instead of an improper fraction?

While $ 13\frac{1}{3} $ equals $ \frac{40}{3} $, it's better to use the improper fraction form for algebraic problems. It makes calculations and verification easier.

Q: What if I get a different equation when I set up the perimeter?

Double-check that you're using all four sides! The perimeter formula for any quadrilateral is the sum of all four side lengths. For this parallelogram: x + 2x + x + 2x = 6x = 80.

Parallelogram Perimeter with Algebraic Expressions

The parallelogram ABCD has a perimeter equal to 80 cm.

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the value of X.

00:10 Remember, the perimeter of a parallelogram is the sum of all its sides.

00:15 In a parallelogram, opposite sides are equal. So, multiply each pair of sides.

00:21 Now, plug in the values you have, and solve for X.

00:26 Next, combine like terms together.

00:30 Then, isolate X to find its value.

00:37 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The parallelogram ABCD has a perimeter equal to 80 cm.

Calculate X.

Step-by-step solution

Since in a parallelogram each pair of opposite sides are equal and parallel:

$BC=AD=2x$

$AB=CD=x$

Now let's substitute the known data into the formula for calculating the perimeter:

$80=2x\times2+2\times x$

$80=4x+2x$

$80=6x$

Let's divide both terms by 6:

$\frac{80}{6}=\frac{6x}{6}$

$\frac{80}{6}=x$

Let's simplify the fraction by 2

$\frac{40}{3}=x$

Final Answer

$x=\frac{40}{3}$

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelogram are equal and parallel
Setup: Perimeter = 2(x) + 2(2x) = 80, so 6x = 80
Check: Substitute $x = \frac{40}{3}$ : sides are $\frac{40}{3}$ and $\frac{80}{3}$ , perimeter = 80 ✓

Common Mistakes

Avoid these frequent errors

Adding sides instead of using perimeter formula
Don't write x + 2x = 80 for the perimeter! This only counts two sides, not all four. A parallelogram has two pairs of equal opposite sides, so you need 2x + 2(2x) = 80. Always multiply each different side length by 2 for the 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 do I multiply by 2 for each side length?

A parallelogram has four sides, but opposite sides are equal. So if one side is x, there are two sides with length x. If another side is 2x, there are two sides with length 2x. That's why the perimeter is 2x + 2(2x).

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

In parallelogram ABCD, AB and CD are opposite (both labeled x), and BC and AD are opposite (both labeled 2x). Opposite sides are the ones that don't share a vertex.

Can I leave my answer as a mixed number instead of an improper fraction?

While $13\frac{1}{3}$ equals $\frac{40}{3}$ , it's better to use the improper fraction form for algebraic problems. It makes calculations and verification easier.

What if I get a different equation when I set up the perimeter?

Double-check that you're using all four sides! The perimeter formula for any quadrilateral is the sum of all four side lengths. For this parallelogram: x + 2x + x + 2x = 6x = 80.

Why is my answer not a whole number?

Not all algebraic solutions are whole numbers! Fractional answers like $\frac{40}{3}$ are completely valid. What matters is that your answer satisfies the original equation when you check it.

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