Rectangle Area Problem: Solve for X When 3(2X + 2) = 24

Q: Why do I need to use parentheses in the area formula?

The width is 2x + 2, which is a complete expression. When multiplying by length (3), you must treat the entire width as one unit: $ 3 \times (2x + 2) $.

Q: What does 'distribute' mean in this problem?

Distributing means multiplying the number outside parentheses by each term inside. So $ 3(2x + 2) = 3 \cdot 2x + 3 \cdot 2 = 6x + 6 $.

Q: How do I know which side is length and which is width?

It doesn't matter! Rectangle area is length × width or width × length - both give the same result. Use whichever setup feels easier.

Q: Can I solve this without distributing first?

Yes! You can divide both sides by 3 first: $ 2x + 2 = 8 $, then solve. Both methods work, but distributing is often clearer for beginners.

Q: What if my rectangle dimensions don't make sense?

Always check that your answer gives positive dimensions. If x = 3, then width = 2(3) + 2 = 8, which is positive and reasonable!

Linear Equations with Rectangle Area Applications

The area of the rectangle below is equal to 24.

AC = 3

AB = 2X + 2

Calculate X.

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Step-by-step video solution

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Step-by-step written solution

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Understand the problem

The area of the rectangle below is equal to 24.

AC = 3

AB = 2X + 2

Calculate X.

Step-by-step solution

The area of the rectangle is equal to the length multiplied by the width.

Let's present the known data:

$24=3\times(2x+2)$

$24=6x+6$

We'll move 6 to the left side and maintain the appropriate sign:

$24-6=6x$

$18=6x$

We'll divide both sides by 6:

$x=3$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Area Formula: Area equals length times width for any rectangle
Algebraic Setup: Set up $3 \times (2x + 2) = 24$ from given dimensions
Verification: Check that $3 \times (2(3) + 2) = 3 \times 8 = 24$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute multiplication across parentheses
Don't just multiply 3 by 2x = 6x and ignore the +2! This gives 6x = 24 instead of 6x + 6 = 24, leading to x = 4 (wrong answer). Always distribute multiplication to every term inside parentheses.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to use parentheses in the area formula?

The width is 2x + 2, which is a complete expression. When multiplying by length (3), you must treat the entire width as one unit: $3 \times (2x + 2)$ .

What does 'distribute' mean in this problem?

Distributing means multiplying the number outside parentheses by each term inside. So $3(2x + 2) = 3 \cdot 2x + 3 \cdot 2 = 6x + 6$ .

How do I know which side is length and which is width?

It doesn't matter! Rectangle area is length × width or width × length - both give the same result. Use whichever setup feels easier.

Can I solve this without distributing first?

Yes! You can divide both sides by 3 first: $2x + 2 = 8$ , then solve. Both methods work, but distributing is often clearer for beginners.

What if my rectangle dimensions don't make sense?

Always check that your answer gives positive dimensions. If x = 3, then width = 2(3) + 2 = 8, which is positive and reasonable!

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