Parallelogram Side Length: Finding Missing Side Given 9cm and 30cm Perimeter

Q: Why can't I just divide 30 by 4 to get each side?

That would only work if it were a rhombus (where all sides are equal). In a regular parallelogram, opposite sides are equal, but adjacent sides can be different lengths.

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

In parallelogram ABCD, sides AB = CD and sides BC = AD. The sides across from each other (opposite sides) are always equal.

Q: Can I use this method for other parallelogram problems?

Absolutely! The formula $ P = 2(a + b) $ works for any parallelogram when you know the perimeter and one side length.

Q: What's the difference between a parallelogram and a rectangle?

A rectangle is a special type of parallelogram where all angles are 90°. Both use the same perimeter formula, but rectangles also have equal opposite sides.

Parallelogram Properties with Perimeter Calculations

A parallelogram has a perimeter of 30 cm.

AB = 9 cm

Calculate the length of 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 parallelograms

00:16 They are also a pair of opposite sides therefore equal

00:20 The perimeter of the parallelogram equals the sum of its sides

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

00:54 Group the numbers into one factor, and BD into one factor

01:04 Isolate BD

01:20 This is the length of BD

01:33 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

A parallelogram has a perimeter of 30 cm.

AB = 9 cm

Calculate the length of the other side.

Step-by-step solution

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

Step 1: Identify the given information and formula.
Step 2: Apply the perimeter formula for a parallelogram.
Step 3: Solve for the unknown side length.

Let's work through each step:

Step 1: We are given that the perimeter of the parallelogram is 30 cm and one side $AB = 9$ cm. We need to find the other side, $b$ .

Step 2: The perimeter formula for a parallelogram is $P = 2(a + b)$ , where $a = 9$ cm and the perimeter $P = 30$ cm.

Step 3: Substitute the known values into the formula:

$30 = 2(9 + b)$

Divide both sides by 2 to simplify:

$15 = 9 + b$

Subtract 9 from both sides to solve for $b$ :

$b = 15 - 9$
$b = 6$

Therefore, the length of the other side is $\text{6 cm}$ .

Thus, the solution to the problem is $b = 6$ cm.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are equal in length
Formula: Perimeter = 2(a + b), so 30 = 2(9 + b)
Check: Verify 2(9 + 6) = 2(15) = 30 cm ✓

Common Mistakes

Avoid these frequent errors

Forgetting opposite sides are equal
Don't assume all four sides could be different lengths = treating it like any quadrilateral! This leads to overcomplicated calculations with too many unknowns. Always remember that parallelograms have two pairs of equal opposite sides.

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 can't I just divide 30 by 4 to get each side?

That would only work if it were a rhombus (where all sides are equal). In a regular parallelogram, opposite sides are equal, but adjacent sides can be different lengths.

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

In parallelogram ABCD, sides AB = CD and sides BC = AD. The sides across from each other (opposite sides) are always equal.

What if I get a decimal or fraction for the side length?

That's completely normal! Side lengths don't have to be whole numbers. Just make sure your answer makes sense - it should be positive and reasonable for the given perimeter.

Can I use this method for other parallelogram problems?

Absolutely! The formula $P = 2(a + b)$ works for any parallelogram when you know the perimeter and one side length.

What's the difference between a parallelogram and a rectangle?

A rectangle is a special type of parallelogram where all angles are 90°. Both use the same perimeter formula, but rectangles also have equal opposite sides.

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