Solve for X: Rectangle with Area 50 and Length 4X

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

In rectangles, length and width are interchangeable - what matters is correctly identifying the two perpendicular sides. From the diagram: AC = 5 and AB = 4X, so Area = 5 × 4X.

Q: Why do I get a decimal answer for X?

Decimal answers are perfectly normal! Since $ 50 ÷ 20 = 2.5 $, this means the side length AB = 4(2.5) = 10 units. Always check that your decimal makes sense.

Q: What if I set up the equation differently?

You might write $ 4X × 5 = 50 $ instead of $ 5 × 4X = 50 $. That's fine! Multiplication is commutative, so both give the same result: X = 2.5.

Q: How do I check if my answer is correct?

Substitute X = 2.5 back into the area formula: $ Area = 5 × 4(2.5) = 5 × 10 = 50 $. Since this matches the given area, your answer is correct!

Q: Can the area ever be negative?

No! Area represents space and must always be positive. If you get a negative result, check your equation setup - you likely made an error in the problem setup or calculation.

Area Equations with Variable Expressions

The area of the rectangle below is equal to 50.

AC = 5

AB = 4X

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the value of X.

00:13 To calculate the area of a rectangle, multiply the width A B by the length A C.

00:18 Now, plug in the given values, and solve for X, step by step.

00:24 Great job! That's how we solve this problem.

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 50.

AC = 5

AB = 4X

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:

$50=5\times4x$

$50=20x$

Let's finish by dividing both sides by 20:

$x=2.5$

Final Answer

2.5

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width: A = l × w
Technique: Substitute known values: 50 = 5 × 4X becomes 50 = 20X
Check: Verify by calculating: 5 × 4(2.5) = 5 × 10 = 50 ✓

Common Mistakes

Avoid these frequent errors

Confusing which sides are length and width
Don't assume AB is always length = wrong area calculation! The diagram shows AC = 5 (height) and AB = 4X (width), so mixing these up gives incorrect equations. Always identify which measurement corresponds to which dimension before setting up your area equation.

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

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

In rectangles, length and width are interchangeable - what matters is correctly identifying the two perpendicular sides. From the diagram: AC = 5 and AB = 4X, so Area = 5 × 4X.

Why do I get a decimal answer for X?

Decimal answers are perfectly normal! Since $50 ÷ 20 = 2.5$ , this means the side length AB = 4(2.5) = 10 units. Always check that your decimal makes sense.

What if I set up the equation differently?

You might write $4X × 5 = 50$ instead of $5 × 4X = 50$ . That's fine! Multiplication is commutative, so both give the same result: X = 2.5.

How do I check if my answer is correct?

Substitute X = 2.5 back into the area formula: $Area = 5 × 4(2.5) = 5 × 10 = 50$ . Since this matches the given area, your answer is correct!

Can the area ever be negative?

No! Area represents space and must always be positive. If you get a negative result, check your equation setup - you likely made an error in the problem setup or calculation.

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