Calculate Parallelogram Side Length: Given 25cm Perimeter and 8cm Side

Q: Why does a parallelogram have only two different side lengths?

In a parallelogram, opposite sides are always equal. So if AB = 8 cm, then CD = 8 cm too. Similarly, BC = AD. This means you only need to find one unknown side length!

Q: Can I use the formula P = 4s like for a square?

No! The formula P = 4s only works for squares where all sides are equal. For parallelograms, use P = 2(a + b) where a and b are the two different side lengths.

Q: How do I know which side is which in the diagram?

Look for the labeled measurements in the diagram. Here, AB is marked as 8 cm. The adjacent side (BC or AD) is what you need to find, and it will be different from AB.

Q: What's the difference between perimeter and area?

Perimeter is the distance around the outside of the shape (like putting a fence around it). Area is the space inside the shape. This problem only asks for perimeter calculations.

Parallelogram Perimeter with Given Side Length

Given the parallelogram whose perimeter is equal to 25 cm and AB=8 cm:

Calculate the other side.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AC

00:03 Opposite sides are equal in a parallelogram

00:18 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 BD

00:54 Let's group the numbers to one factor, and BD to one factor

01:02 Let's isolate BD

01:17 This is the length of BD

01:28 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

Given the parallelogram whose perimeter is equal to 25 cm and AB=8 cm:

Calculate the other side.

Step-by-step solution

Let's solve this problem step-by-step:

Step 1: Understand the problem
We are given the perimeter of the parallelogram as 25 cm and one side $AB$ as 8 cm. We need to calculate the length of the other side of the parallelogram, $BC$ .
Step 2: Recall the formula for the perimeter of a parallelogram
The perimeter $P$ of a parallelogram is given by:
$P = 2(a + b)$
Where $a$ and $b$ are lengths of adjacent sides.
Step 3: Apply the given information
We have $P = 25$ cm and one side $a = AB = 8$ cm. Substitute these into the formula:
$25 = 2(8 + b)$
Step 4: Solve for the unknown side $b$
First, divide both sides by 2:
$12.5 = 8 + b$
Subtract 8 from both sides:
$b = 12.5 - 8$
$b = 4.5$
Therefore, the length of the other side is $4.5$ cm.

Upon checking with the given choices, the correct answer is indeed 4.5.

Final Answer

4.5

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: P = 2(a + b) for parallelogram sides
Technique: Substitute known values: 25 = 2(8 + b)
Check: Verify: 2(8 + 4.5) = 2(12.5) = 25 cm ✓

Common Mistakes

Avoid these frequent errors

Forgetting that opposite sides are equal in a parallelogram
Don't assume all four sides are different lengths = overcomplicated solution! This leads to setting up wrong equations with four unknowns. Always remember that opposite sides of a parallelogram are equal, so you only need to find one unknown side.

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 a parallelogram have only two different side lengths?

In a parallelogram, opposite sides are always equal. So if AB = 8 cm, then CD = 8 cm too. Similarly, BC = AD. This means you only need to find one unknown side length!

Can I use the formula P = 4s like for a square?

No! The formula P = 4s only works for squares where all sides are equal. For parallelograms, use P = 2(a + b) where a and b are the two different side lengths.

What if I get a decimal answer?

Decimal answers are perfectly normal for parallelogram problems! In this case, 4.5 cm is the correct answer. Always double-check by substituting back into the perimeter formula.

How do I know which side is which in the diagram?

Look for the labeled measurements in the diagram. Here, AB is marked as 8 cm. The adjacent side (BC or AD) is what you need to find, and it will be different from AB.

What's the difference between perimeter and area?

Perimeter is the distance around the outside of the shape (like putting a fence around it). Area is the space inside the shape. This problem only asks for perimeter calculations.

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