Calculate Rectangle Perimeter: Finding the Distance When Width is X-2

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

A rectangle has 4 sides: 2 lengths and 2 widths. The formula $ P = 2(\text{length} + \text{width}) $ accounts for both pairs of equal sides efficiently!

Q: How do I handle the (X - 2) expression?

Treat $ X - 2 $ as a single unit representing the width. When adding $ X + (X - 2) $, combine like terms: $ X + X - 2 = 2X - 2 $.

Q: What if I get confused with the algebra?

Work step by step: First add inside parentheses, then multiply by 2. Don't try to do everything at once - break it into smaller, manageable steps!

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

Try substituting a simple value like $ X = 5 $. Length = 5, Width = 3, so Perimeter = $ 2(5 + 3) = 16 $. Using our formula: $ 4(5) - 4 = 16 $ ✓

Q: Why isn't the answer 2X - 2?

$ 2X - 2 $ is just length + width, but perimeter needs all four sides. You must multiply this sum by 2 to get the complete perimeter: $ 4X - 4 $.

Rectangle Perimeter with Variable Expressions

Calculate the perimeter of the rectangle:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the rectangle's perimeter

00:03 Apply the formula for calculating the perimeter of a rectangle- 2 x the sum of its sides

00:09 Solve what's inside the parentheses first

00:14 Open the parentheses - multiply each factor

00:17 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the perimeter of the rectangle:

Step-by-step solution

To solve this problem, we need to find the perimeter of a rectangle with given dimensions. The formula for the perimeter $P$ is:

$P = 2(\text{length} + \text{width})$

In this problem, we are given:

Length $= X$
Width $= X - 2$

Using the perimeter formula, we substitute the given values:

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

First, simplify the expression within the parentheses:

$X + (X - 2) = X + X - 2 = 2X - 2$

Now substitute back to find the perimeter:

$P = 2(2X - 2)$

Distribute the 2 to both terms inside the parentheses:

$P = 4X - 4$

Therefore, the perimeter of the rectangle is $4X - 4$ .

The correct choice corresponding to this calculation is: $4X - 4$ .

Final Answer

$4x-4$

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals 2 times length plus width
Technique: Substitute $X$ and $X-2$ into $P = 2(\text{length} + \text{width})$
Check: Distribute 2 through parentheses: $2(2X - 2) = 4X - 4$ ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of using perimeter formula
Don't just add X + (X - 2) = 2X - 2! This only gives you the sum of two sides, not the complete perimeter. Always use P = 2(length + width) to account for all four sides of the rectangle.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do I multiply by 2 in the perimeter formula?

A rectangle has 4 sides: 2 lengths and 2 widths. The formula $P = 2(\text{length} + \text{width})$ accounts for both pairs of equal sides efficiently!

How do I handle the (X - 2) expression?

Treat $X - 2$ as a single unit representing the width. When adding $X + (X - 2)$ , combine like terms: $X + X - 2 = 2X - 2$ .

What if I get confused with the algebra?

Work step by step: First add inside parentheses, then multiply by 2. Don't try to do everything at once - break it into smaller, manageable steps!

How can I check if 4X - 4 is correct?

Try substituting a simple value like $X = 5$ . Length = 5, Width = 3, so Perimeter = $2(5 + 3) = 16$ . Using our formula: $4(5) - 4 = 16$ ✓

Why isn't the answer 2X - 2?

$2X - 2$ is just length + width, but perimeter needs all four sides. You must multiply this sum by 2 to get the complete perimeter: $4X - 4$ .

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