Solve for X: Rectangle Area 48 with Height 4 and Width 2X

Q: Why do I multiply 4 and 2X instead of adding them?

Area is always length × width, never length + width. Adding gives you perimeter (the distance around), but multiplying gives you the space inside the rectangle.

Q: How do I solve 8X = 48?

Divide both sides by 8: $ \frac{8X}{8} = \frac{48}{8} $. The 8's cancel on the left, giving you X = 6.

Rectangle Area with Algebraic Dimensions

The area of the rectangle below is equal to 48.

AC = 4

AB = 2X

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the value of X

00:03 The formula for calculating the area of a rectangle is width(AB) multiplied by length(AC)

00:07 Substitute in the relevant values according to the given data and solve for X

00:14 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the rectangle below is equal to 48.

AC = 4

AB = 2X

Calculate X.

Step-by-step solution

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

Let's begin by presenting the known data:

$48=4\times2x$

$48=8x$

Lastly let's divide both sides by 8:

$x=6$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width (A = l × w)
Technique: Substitute known values: 48 = 4 × 2X becomes 48 = 8X
Check: Verify by calculating: 4 × (2 × 6) = 4 × 12 = 48 ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate 4 + 2X = 48 to find X! Area requires multiplication, not addition. This gives X = 22, but checking: 4 × 44 = 176 ≠ 48. Always multiply length times width for area.

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 4 and 2X instead of adding them?

Area is always length × width, never length + width. Adding gives you perimeter (the distance around), but multiplying gives you the space inside the rectangle.

What does 2X mean in this problem?

2X means 2 times the value of X. So if X = 6, then 2X = 2 × 6 = 12. It's not 2 + X, it's 2 multiplied by X.

How do I solve 8X = 48?

Divide both sides by 8: $\frac{8X}{8} = \frac{48}{8}$ . The 8's cancel on the left, giving you X = 6.

Can I check my answer a different way?

Yes! Calculate the actual dimensions: height = 4, width = 2X = 2(6) = 12. Then verify: 4 × 12 = 48 ✓

What if I got a different answer?

Double-check your setup: Area = length × width, so 48 = 4 × 2X. Then simplify: 48 = 8X. Finally divide: X = 48 ÷ 8 = 6. Always substitute back to verify!

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