Parallelogram Side Length: Finding AB When 3X=6 and Perimeter=40cm

Q: Why can I assume AB = CD in a parallelogram?

This is a fundamental property of parallelograms! Opposite sides are always equal in length. So if you know one side, you automatically know its opposite side too.

Q: Can I use the perimeter formula P = AB + BC + CD + AD?

Yes, but it's more complex! Since opposite sides are equal, you'd have: P = AB + BC + AB + BC = 2AB + 2BC. The formula $ P = 2(AB + BC) $ is much simpler.

Parallelogram Perimeter with Variable Expressions

Given the parallelogram ABCD whose perimeter is equal to 40 cm, it is also known that X=2

According to the data in the drawing, find a AB

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AB

00:04 The perimeter of the parallelogram equals the sum of the sides

00:07 Opposite sides are equal in a parallelogram, so multiply each side

00:12 Substitute appropriate values according to the given data, and solve for AB

00:26 Substitute the value of X

00:32 Isolate AB

00:40 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

Given the parallelogram ABCD whose perimeter is equal to 40 cm, it is also known that X=2

According to the data in the drawing, find a AB

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Calculate the length of $CD$ using the given $X = 2$ .
Step 2: Use the perimeter formula for the parallelogram to find $AB$ .
Step 3: Solve for the unknown length $AB$ .

Step 1: Calculate the length of $CD$ .

Given $X = 2$ , we find $CD = 3X = 3 \times 2 = 6$ cm.

Step 2: Use the formula for the perimeter of a parallelogram:
$P = 2 \times (AB + CD)$ .

Substitute the given values:
$40 = 2 \times (AB + 6)$ .

Step 3: Solve for $AB$ .

Start by dividing the entire equation by 2:
$20 = AB + 6$ .

Subtract 6 from both sides to isolate $AB$ :
$AB = 20 - 6 = 14$ .

Therefore, the length of side $AB$ is $14$ cm.

Final Answer

$14$

Key Points to Remember

Essential concepts to master this topic

Parallelogram Property: Opposite sides are equal, so AB = CD
Technique: Calculate CD = 3X = 3(2) = 6, then use perimeter formula
Check: Verify P = 2(14 + 6) = 2(20) = 40 cm ✓

Common Mistakes

Avoid these frequent errors

Forgetting opposite sides are equal in parallelograms
Don't assume all four sides are different lengths = complex equations with too many unknowns! This makes the problem unsolvable. Always remember that in parallelograms, opposite sides are equal: AB = CD and BC = AD.

Practice Quiz

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Find the perimeter of the parallelogram using the data below.

FAQ

Everything you need to know about this question

Why can I assume AB = CD in a parallelogram?

This is a fundamental property of parallelograms! Opposite sides are always equal in length. So if you know one side, you automatically know its opposite side too.

What if X wasn't given as 2?

The same method works! First substitute the given value of X into $3X$ to find CD, then use the perimeter formula $P = 2(AB + CD)$ to solve for AB.

Can I use the perimeter formula P = AB + BC + CD + AD?

Yes, but it's more complex! Since opposite sides are equal, you'd have: P = AB + BC + AB + BC = 2AB + 2BC. The formula $P = 2(AB + BC)$ is much simpler.

How do I know which sides are opposite?

In parallelogram ABCD, the vertices are labeled in order around the shape. So AB is opposite to CD, and BC is opposite to AD. Think of it as sides that don't share a vertex.

What if the diagram shows different expressions on other sides?

Use the same approach! Identify which sides are opposite, substitute any given values, then set up your perimeter equation. The key is recognizing that opposite sides must be equal.

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