Calculate Parallelogram Side Length: Given Perimeter 20cm and Side 7cm

Q: Why is the perimeter formula 2(a + b) instead of a + b + c + d?

In a parallelogram, opposite sides are equal! So if AB = 7 cm, then CD = 7 cm too. Similarly, if AD = 3 cm, then BC = 3 cm. That's why we only need two different side lengths.

Q: What if I'm given the perimeter and need both side lengths?

You need at least one side length to find the other. If you only know the perimeter, there are infinitely many possible parallelograms with different side combinations.

Q: Do all parallelograms follow this same perimeter rule?

Yes! This includes rectangles, squares, and rhombuses - they're all special types of parallelograms. The formula $ 2(a + b) $ works for all of them.

Q: How do I set up the equation when solving for the unknown side?

Start with the perimeter formula: $ 2(a + b) = 20 $. Substitute what you know: $ 2(7 + b) = 20 $. Then solve step by step using algebra.

Q: What's the difference between adjacent and opposite sides?

Adjacent sides share a corner (like AB and AD), while opposite sides are across from each other (like AB and CD). In our formula, a and b represent adjacent sides.

Parallelogram Perimeter with Side Length Calculation

A parallelogram has a perimeter of 20 cm

AB = 7 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 a parallelogram

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

00:21 The perimeter of the parallelogram equals the sum of its sides

00:37 Let's substitute appropriate values and solve for BD

00:57 Group the numbers into one factor, and BD into another factor

01:05 Isolate BD

01:20 This is the length of BD

01:26 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 20 cm

AB = 7 cm

Calculate the length of the other side.

Step-by-step solution

To solve the problem, we'll proceed as follows:

Step 1: Identify the known values and write down the perimeter formula: The perimeter of a parallelogram is $2(a + b)$ , where $a = 7$ cm is the known side, and $b$ is the unknown side.
Step 2: Substitute the known perimeter into the formula: We know that $2(a + b) = 20$ .
Step 3: Set up the equation with known values: $2(7 + b) = 20$ .
Step 4: Solve the equation for $b$ : Start by simplifying $2(7 + b) = 20$ to $14 + 2b = 20$ .
Step 5: Subtract 14 from both sides to isolate $2b$ : $2b = 20 - 14$ . Thus, $2b = 6$ .
Step 6: Divide both sides by 2 to solve for $b$ : $b = \frac{6}{2} = 3$ cm.

Therefore, the length of the other side is $3$ cm.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Parallelogram perimeter equals 2(a + b) where opposite sides are equal
Technique: Substitute known values: 2(7 + b) = 20, then solve for b
Check: Verify answer: 2(7 + 3) = 2(10) = 20 cm ✓

Common Mistakes

Avoid these frequent errors

Using incorrect perimeter formula
Don't use 4a or a + b + c + d = wrong formula! Parallelograms have two pairs of equal opposite sides, not four different sides. Always use 2(a + b) where a and b are adjacent 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 is the perimeter formula 2(a + b) instead of a + b + c + d?

In a parallelogram, opposite sides are equal! So if AB = 7 cm, then CD = 7 cm too. Similarly, if AD = 3 cm, then BC = 3 cm. That's why we only need two different side lengths.

What if I'm given the perimeter and need both side lengths?

You need at least one side length to find the other. If you only know the perimeter, there are infinitely many possible parallelograms with different side combinations.

Do all parallelograms follow this same perimeter rule?

Yes! This includes rectangles, squares, and rhombuses - they're all special types of parallelograms. The formula $2(a + b)$ works for all of them.

How do I set up the equation when solving for the unknown side?

Start with the perimeter formula: $2(a + b) = 20$ . Substitute what you know: $2(7 + b) = 20$ . Then solve step by step using algebra.

What's the difference between adjacent and opposite sides?

Adjacent sides share a corner (like AB and AD), while opposite sides are across from each other (like AB and CD). In our formula, a and b represent adjacent sides.

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