Rectangle Area Problem: Find Side Length AB When Area = 24 and AC = 3

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

In rectangles, it doesn't matter! Length × width = width × length because multiplication is commutative. Just make sure you use the correct measurements for each side.

Q: Why do we divide 24 by 3 instead of adding?

Because area uses multiplication, not addition! When you know Area = AB × AC and need to find AB, you must divide the area by AC to isolate AB.

Q: Can I use this method for any rectangle?

Yes! The formula Area = length × width works for all rectangles. If you know the area and one side, you can always find the other side by division.

Rectangle Area Formula with Given Dimensions

The area of the rectangle below is equal to 24.

AC = 3

What is the length of side AB?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the value of AB

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 AB

00:13 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 24.

AC = 3

What is the length of side AB?

Step-by-step solution

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

Let's begin by inserting the known data into the formula:

$S=AB\times AC$

$24=AB\times3$

Let's now divide both sides by 3:

$AB=8$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width
Technique: Rearrange 24 = AB × 3 to AB = 24 ÷ 3
Check: Verify 8 × 3 = 24 confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Confusing which sides to multiply
Don't assume AB is the width when AC might be given = wrong setup! Students often mix up which dimension goes where in the formula. Always identify which sides are length and width, then use Area = length × width consistently.

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! Length × width = width × length because multiplication is commutative. Just make sure you use the correct measurements for each side.

Why do we divide 24 by 3 instead of adding?

Because area uses multiplication, not addition! When you know Area = AB × AC and need to find AB, you must divide the area by AC to isolate AB.

What if the area was a fraction or decimal?

The same method works! Just divide the area by the known side length. For example, if area = 15.5 and one side = 3.1, then the other side = 15.5 ÷ 3.1 = 5.

Can I use this method for any rectangle?

Yes! The formula Area = length × width works for all rectangles. If you know the area and one side, you can always find the other side by division.

How do I check if my answer makes sense?

Multiply your answer by the given side length. If you get the original area, you're correct! Also, make sure your answer is positive since lengths can't be negative.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Rectangles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime