Solve for X: Rectangle with Width 8cm and Area 32cm²

Q: Why do we multiply length by width for area?

Area measures how much space is inside a shape. When you multiply length by width, you're counting how many unit squares fit inside the rectangle - that's the total area!

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

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

Q: Can I solve this without algebra?

Yes! You can think: "What number times 8 equals 32?" But algebra helps you organize your thinking and works for harder problems too.

Q: What if the answer isn't a whole number?

That's totally normal! Many rectangles have fractional or decimal dimensions. Just make sure your answer makes the area equation true when you check it.

Q: How do I know which measurement is length vs width?

For area calculations, it doesn't matter! $ 8 \times 4 = 4 \times 8 = 32 $. The multiplication is commutative, so you'll get the same answer either way.

Rectangle Area with Algebraic Length

The width of a rectangle is equal to
$8$ cm and its length is $x$ cm.

The area of the rectangle is $32$ cm².

Calculate $x$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate X

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

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

00:12 Isolate X

00:15 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
$8$ cm and its length is $x$ cm.

The area of the rectangle is $32$ cm².

Calculate $x$ .

Step-by-step solution

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

Let's first input the known data into the formula:

$32=8x$

Let's now reduce both sides of the equation by the (HCF) highest common factor 8:

$x=4$

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: 32 = 8 × x, then solve
Check: Verify by calculating: 8 × 4 = 32 cm² ✓

Common Mistakes

Avoid these frequent errors

Adding width and length instead of multiplying
Don't calculate 8 + x = 32 to get x = 24! Addition gives perimeter, not area. Area always requires multiplication. Always use A = length × width for rectangle area problems.

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 we multiply length by width for area?

Area measures how much space is inside a shape. When you multiply length by width, you're counting how many unit squares fit inside the rectangle - that's the total area!

What's the difference between area and perimeter?

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

Can I solve this without algebra?

Yes! You can think: "What number times 8 equals 32?" But algebra helps you organize your thinking and works for harder problems too.

What if the answer isn't a whole number?

That's totally normal! Many rectangles have fractional or decimal dimensions. Just make sure your answer makes the area equation true when you check it.

How do I know which measurement is length vs width?

For area calculations, it doesn't matter! $8 \times 4 = 4 \times 8 = 32$ . The multiplication is commutative, so you'll get the same answer either way.

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