Parallelogram ABCD: Finding Side Length BC with 35cm Perimeter

Q: Why can't I just divide the perimeter by 4 to find each side?

Because parallelograms don't have all four sides equal (that's only true for squares)! A parallelogram has two pairs of equal opposite sides, so you need the formula $ P = 2(a + b) $.

Q: How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in parallelograms. So AB = CD and BC = AD. This is why we only need to find two different side lengths.

Q: Can I solve this without the perimeter formula?

Yes, but it's much harder! You could set up 35 = AB + BC + CD + DA, then substitute equal sides, but the formula $ P = 2(a + b) $ makes it much simpler.

Q: How do I check if my answer makes sense?

Ask yourself: Are the two side lengths reasonable? Here, 9.5 cm and 8 cm are close but different, which makes sense for a parallelogram that's not a rectangle.

Parallelogram Perimeter with Unknown Side

Shown below is the parallelogram ABCD, which has a perimeter of 35 cm.

What is the length of the side BC?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find BC

00:04 Opposite sides are equal in a parallelogram

00:14 Let's mark the unknown sides with X

00:23 The perimeter of the parallelogram equals the sum of sides

00:33 Let's substitute appropriate values according to the given data and solve for X

01:05 Isolate X

01:16 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

Shown below is the parallelogram ABCD, which has a perimeter of 35 cm.

What is the length of the side BC?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us that the parallelogram has a total perimeter of 35 cm and one side $AB = 9.5$ cm.
Step 2: We'll use the formula for the perimeter of a parallelogram: $P = 2(a + b)$ , where $a$ and $b$ are adjacent sides. Here, given that $AB = 9.5$ cm, we have $a = 9.5$ cm.
Step 3: Substitute the known values into the formula:
$35 = 2(9.5 + b)$
Divide both sides by 2:
$17.5 = 9.5 + b$
Solve for $b$ :
$b = 17.5 - 9.5 = 8$

Therefore, the length of side $BC$ is $\mathbf{8}$ cm.

Final Answer

8 cm

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are equal in length
Formula: Perimeter = 2(a + b) where a and b are adjacent sides
Check: Verify: 2(9.5 + 8) = 2(17.5) = 35 cm ✓

Common Mistakes

Avoid these frequent errors

Using wrong perimeter formula for parallelograms
Don't add all four sides separately like P = AB + BC + CD + DA = 9.5 + b + 9.5 + b! This makes the problem unnecessarily complicated and prone to errors. Always use the parallelogram formula P = 2(a + b) since opposite sides are equal.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the parallelogram using the data below.

FAQ

Everything you need to know about this question

Why can't I just divide the perimeter by 4 to find each side?

Because parallelograms don't have all four sides equal (that's only true for squares)! A parallelogram has two pairs of equal opposite sides, so you need the formula $P = 2(a + b)$ .

How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in parallelograms. So AB = CD and BC = AD. This is why we only need to find two different side lengths.

What if the diagram shows a different side length?

Use whatever side length is given in the diagram! In this problem, AB = 9.5 cm is shown, so we use that as our known side and solve for the adjacent side BC.

Can I solve this without the perimeter formula?

Yes, but it's much harder! You could set up 35 = AB + BC + CD + DA, then substitute equal sides, but the formula $P = 2(a + b)$ makes it much simpler.

How do I check if my answer makes sense?

Ask yourself: Are the two side lengths reasonable? Here, 9.5 cm and 8 cm are close but different, which makes sense for a parallelogram that's not a rectangle.

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