Rectangle Area: Solving with Width x and Length x/2 When x=4

Q: Do I need to simplify x²/2 before substituting?

You can do either! You can substitute x = 4 first to get 4²/2 = 16/2 = 8, or simplify to get x²/2 then substitute. Both methods give the same answer.

Q: What's the difference between area and perimeter?

Area measures the space inside (length × width), while perimeter measures the distance around the outside (2 × length + 2 × width). Don't confuse them!

Q: Why is the length x/2 instead of just x?

The problem states that the length is half the width. Since width = x, then length = x ÷ 2 = $ \frac{x}{2} $. This makes the rectangle twice as wide as it is long.

Rectangle Area with Variable Expressions

The width of a rectangle is equal to $x$ cm and its length is equal to $\frac{x}{2}$ cm.

$x=4$

What is the area of the rectangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the rectangle's area

00:03 Apply the formula for calculating the area of a rectangle (side x side)

00:09 Substitute in the X value according to the given data and solve for the area

00:17 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The width of a rectangle is equal to $x$ cm and its length is equal to $\frac{x}{2}$ cm.

$x=4$

What is the area of the rectangle?

Step-by-step solution

The area of a rectangle is its length multiplied by its width.

Let's put the data into the formula:

$S=x\times\frac{x}{2}=\frac{x^2}{2}$

Since we know that $x$ equals 4, we can substitute it into the formula and solve accordingly:

$S=\frac{4^2}{2}=\frac{16}{2}=8$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width
Substitution: Replace x with 4: $\frac{4^2}{2} = \frac{16}{2} = 8$
Check: Width = 4 cm, length = 2 cm, area = 8 cm² ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying dimensions
Don't add width + length to find area = 4 + 2 = 6! This gives perimeter, not area. Always multiply length × width for rectangle area.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do I substitute x = 4 into the area formula?

The area formula contains the variable x, but we need a numerical answer. Since we're given that x = 4, we substitute this value to get a concrete result in square centimeters.

Do I need to simplify x²/2 before substituting?

You can do either! You can substitute x = 4 first to get 4²/2 = 16/2 = 8, or simplify to get x²/2 then substitute. Both methods give the same answer.

What's the difference between area and perimeter?

Area measures the space inside (length × width), while perimeter measures the distance around the outside (2 × length + 2 × width). Don't confuse them!

Why is the length x/2 instead of just x?

The problem states that the length is half the width. Since width = x, then length = x ÷ 2 = $\frac{x}{2}$ . This makes the rectangle twice as wide as it is long.

How do I check if my area calculation is correct?

Substitute back: if x = 4, then width = 4 cm and length = 4/2 = 2 cm. Area = 4 × 2 = 8 cm². This matches our formula result!

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