Calculate Rectangle Side Length: Finding AB When Area = 27 and Height = 3

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

In rectangles, it doesn't matter which you call length or width! What matters is that you multiply two perpendicular (adjacent) sides, not parallel ones.

Q: Why do we divide 27 by 3 instead of adding?

Because area uses multiplication! If Area = length × width, then to find length, we divide: length = Area ÷ width. So AB = 27 ÷ 3 = 9.

Q: Can I use this method for any rectangle problem?

Yes! The formula $ A = l \times w $ works for all rectangles. Just substitute what you know and solve for what you don't know.

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

Multiply your answer by the known side: 9 × 3 = 27. If this equals the given area, you're right!

Rectangle Area Formula with Known Dimensions

The area of the rectangle below is equal to 27.

AC = 3

Calculate AB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the value of A B.

00:09 The area of a rectangle is its width, A B, times its length, A C.

00:15 Use the given numbers to solve for A B.

00:20 And there you have 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 27.

AC = 3

Calculate AB.

Step-by-step solution

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

Let's insert the known data into the formula as follows:

$S=AB\times AC$

$27=AB\times3$

Finally let's divide both sides by 3:

$AB=9$

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: 27 = AB × 3, then solve
Check: Verify by multiplying: 9 × 3 = 27 ✓

Common Mistakes

Avoid these frequent errors

Confusing which sides to multiply
Don't randomly multiply any two measurements = wrong area calculation! Students often mix up adjacent vs opposite sides. Always identify length and width as perpendicular sides, then use Area = length × width.

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

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

In rectangles, it doesn't matter which you call length or width! What matters is that you multiply two perpendicular (adjacent) sides, not parallel ones.

Why do we divide 27 by 3 instead of adding?

Because area uses multiplication! If Area = length × width, then to find length, we divide: length = Area ÷ width. So AB = 27 ÷ 3 = 9.

What if I get a decimal or fraction answer?

That's perfectly normal! Rectangle sides can be any positive number. Just make sure your answer makes sense when you check: side × 3 should equal 27.

Can I use this method for any rectangle problem?

Yes! The formula $A = l \times w$ works for all rectangles. Just substitute what you know and solve for what you don't know.

How do I check if my answer is correct?

Multiply your answer by the known side: 9 × 3 = 27. If this equals the given area, you're right!

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