Parallelogram Perimeter Problem: Find X When AB = 6 and Perimeter = 20

Q: Why are opposite sides equal in a parallelogram?

By definition, a parallelogram has parallel opposite sides. This geometry property guarantees that opposite sides are not only parallel but also equal in length.

Q: What if the diagram looks like a rectangle?

A rectangle is a special type of parallelogram! All rectangles have the same opposite-sides-equal property, so you solve it exactly the same way.

Q: How do I set up the perimeter equation?

Perimeter means add all four sides: AB + BC + CD + DA. Since opposite sides are equal, this becomes: $ AB + AC + AB + AC = 2(AB) + 2(AC) $

Parallelogram Perimeter with Opposite Side Properties

Look at the parallelogram shown below.

AB = 6

AC = X

The perimeter of the parallelogram is 20.

Find X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Opposite sides are equal in a parallelogram

00:12 They are also a pair of opposite sides, therefore equal

00:24 The perimeter of the parallelogram equals the sum of its sides

00:38 Let's substitute appropriate values and solve for X

00:54 Isolate X

01:02 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the parallelogram shown below.

AB = 6

AC = X

The perimeter of the parallelogram is 20.

Find X.

Step-by-step solution

As is true for a parallelogram each pair of opposite sides are equal:

$AB=CD=6,AC=BD=x$

Calculate X according to the given perimeter:

$20=6+6+x+x$

$20=12+2x$

$20-12=2x$

$8=2x$

$x=4$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Opposite sides of a parallelogram are always equal in length
Technique: Use perimeter = 2(side1) + 2(side2), so 20 = 2(6) + 2(x)
Check: Verify perimeter: 6 + 4 + 6 + 4 = 20 ✓

Common Mistakes

Avoid these frequent errors

Forgetting that opposite sides are equal
Don't assume all four sides are different lengths = overcomplicated equation! In parallelograms, opposite sides AB = CD and AC = BD are always equal. Always use the property that opposite sides are identical to set up your equation with just two unknowns.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.

FAQ

Everything you need to know about this question

Why are opposite sides equal in a parallelogram?

By definition, a parallelogram has parallel opposite sides. This geometry property guarantees that opposite sides are not only parallel but also equal in length.

Can I solve this without using the opposite sides property?

You could try, but it would be much harder! Without knowing opposite sides are equal, you'd have four different variables instead of just two, making the problem unsolvable with the given information.

What if the diagram looks like a rectangle?

A rectangle is a special type of parallelogram! All rectangles have the same opposite-sides-equal property, so you solve it exactly the same way.

How do I set up the perimeter equation?

Perimeter means add all four sides: AB + BC + CD + DA. Since opposite sides are equal, this becomes: $AB + AC + AB + AC = 2(AB) + 2(AC)$

What if I get a decimal or fraction for X?

That's totally fine! Geometric measurements don't have to be whole numbers. Just make sure your answer makes sense when you check the perimeter calculation.

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