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

Find the perimeter of the parallelogram using the data below.

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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