Parallelogram Perimeter: Expressing Length X + (X+4) Solution

Q: Why do we multiply by 2 in the perimeter formula?

A parallelogram has 4 sides, but opposite sides are equal. So instead of adding all 4 sides individually, we can add the 2 different side lengths and multiply by 2: P = 2(a + b).

Q: How do I know which side is X and which is X+4?

The problem states that X is the smaller side. Since one side is 4 units greater than the other, the sides are X (smaller) and X+4 (larger). The formula works regardless of which side you call 'a' or 'b'.

Q: Can I solve this by adding X + X + (X+4) + (X+4)?

Absolutely! That's another correct approach: $ X + X + (X+4) + (X+4) = 2X + 2X + 8 = 4X + 8 $. This gives the same result as using the formula P = 2(a + b).

Q: How can I check if 4X + 8 is correct?

Use the distributive property backwards: $ 4X + 8 = 4(X + 2) $. Or substitute a test value like X = 1: sides are 1 and 5, so perimeter = $ 2(1 + 5) = 12 $, and $ 4(1) + 8 = 12 $ ✓

Parallelogram Perimeter with Variable Expressions

Given a parallelogram where the length of one side is greater by 4 than the length of another side and given that the length of the smaller side is X:

Express by X the perimeter of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's express the perimeter of the parallelogram using the variable X.

00:17 Remember, opposite sides are equal in a parallelogram.

00:25 Let's look at the larger pair of sides.

00:29 Here, the side length is given in the problem.

00:37 We also have a side ratio provided in the problem.

00:41 Now, let's substitute the side value to calculate side AB.

00:48 Again, note that opposite sides are equal in a parallelogram.

00:57 The perimeter is the sum of all sides of the parallelogram.

01:12 Insert the given values and solve for the perimeter.

01:20 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given a parallelogram where the length of one side is greater by 4 than the length of another side and given that the length of the smaller side is X:

Express by X the perimeter of the parallelogram.

Step-by-step solution

To solve the problem, we'll apply the perimeter formula for a parallelogram. We are given that one side $a = X$ and the other side $b = X + 4$ . The perimeter $P$ of a parallelogram is calculated by the formula:

$P = 2(a + b)$

Substitute the values of $a$ and $b$ :
$a = X$
$b = X + 4$

Plug these into the formula:

$P = 2(X + (X + 4))$

Simplify the expression inside the parentheses:

$P = 2(2X + 4)$

Distribute the 2:

$P = 4X + 8$

Therefore, the perimeter of the parallelogram in terms of $X$ is $4X + 8$ .

Final Answer

4X+8

Key Points to Remember

Essential concepts to master this topic

Formula: Parallelogram perimeter equals 2 times sum of adjacent sides
Technique: Substitute X and X+4 into P = 2(a + b)
Check: Verify 4X+8 = 2(X) + 2(X+4) = 2X + 2X + 8 ✓

Common Mistakes

Avoid these frequent errors

Adding sides only once instead of doubling
Don't calculate X + (X+4) = 2X+4 as the final answer! This only accounts for two adjacent sides, not the full perimeter. Always remember that parallelograms have 4 sides total, so multiply by 2: P = 2(X + X+4) = 4X+8.

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 do we multiply by 2 in the perimeter formula?

A parallelogram has 4 sides, but opposite sides are equal. So instead of adding all 4 sides individually, we can add the 2 different side lengths and multiply by 2: P = 2(a + b).

How do I know which side is X and which is X+4?

The problem states that X is the smaller side. Since one side is 4 units greater than the other, the sides are X (smaller) and X+4 (larger). The formula works regardless of which side you call 'a' or 'b'.

Can I solve this by adding X + X + (X+4) + (X+4)?

Absolutely! That's another correct approach: $X + X + (X+4) + (X+4) = 2X + 2X + 8 = 4X + 8$ . This gives the same result as using the formula P = 2(a + b).

What if X has a specific value like X = 5?

Then you can find the actual perimeter! With X = 5, the sides would be 5 and 9 units, giving perimeter = $4(5) + 8 = 28$ units. But the question asks for the general expression in terms of X.

How can I check if 4X + 8 is correct?

Use the distributive property backwards: $4X + 8 = 4(X + 2)$ . Or substitute a test value like X = 1: sides are 1 and 5, so perimeter = $2(1 + 5) = 12$ , and $4(1) + 8 = 12$ ✓

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