Solve for X: Rectangle Area 30 with Side Length 2X and Height 3

Q: Why do I multiply 3 and 2x instead of adding them?

For rectangles, area = length × width, not length + width. Adding dimensions gives you the perimeter, which is completely different! Always multiply for area problems.

Q: Can I solve this without using the area formula?

No! The area formula is essential for this type of problem. Without A = l × w, you can't connect the given area (30) to the unknown variable x.

Q: What if the dimensions were switched around?

It doesn't matter! Since multiplication is commutative, 3 × 2x gives the same result as 2x × 3. The area stays 30 either way.

Rectangle Area Formula with Linear Equations

The area of the rectangle below is equal to 30.

AC = 3

AB = 2X

Calculate X.

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Understand the problem

The area of the rectangle below is equal to 30.

AC = 3

AB = 2X

Calculate X.

Step-by-step solution

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

We begin by inserting the given data into this formula:

$30=3\times2x$

$30=6x$

Lastly we divide both sides by 6:

$x=5$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width (A = l × w)
Technique: Substitute known values: 30 = 3 × 2x becomes 30 = 6x
Check: Verify by substituting: 3 × (2×5) = 3 × 10 = 30 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply both dimensions
Don't just set 30 = 2x and solve directly = x = 15! This ignores the height dimension completely. Always multiply length times width: 30 = 3 × 2x.

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 multiply 3 and 2x instead of adding them?

For rectangles, area = length × width, not length + width. Adding dimensions gives you the perimeter, which is completely different! Always multiply for area problems.

Can I solve this without using the area formula?

No! The area formula is essential for this type of problem. Without A = l × w, you can't connect the given area (30) to the unknown variable x.

What if the dimensions were switched around?

It doesn't matter! Since multiplication is commutative, 3 × 2x gives the same result as 2x × 3. The area stays 30 either way.

How do I know which side is length vs width?

In rectangle area problems, it doesn't matter which is length or width. Just make sure to multiply both given dimensions together to get the area!

What if I got x = 15 instead of x = 5?

You likely forgot to include the height! Check your work: if 30 = 2x, then x = 15. But the correct setup is 30 = 3 × 2x = 6x, so x = 5.

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