Find Rectangle Side Length: Area 84 and Height 7 Problem

Q: Why do I multiply the sides instead of adding them?

Area measures how much space is inside the rectangle, which requires multiplication. Adding gives you perimeter (distance around the outside). Think of area as counting squares: 12 rows of 7 squares each!

Q: How do I solve AB × 7 = 84?

Divide both sides by 7: $ \frac{AB \times 7}{7} = \frac{84}{7} $. The 7s cancel on the left, giving you AB = 12.

Q: Can I use different letters instead of AB and AC?

Yes! The letters are just labels for the sides. You might see l and w for length and width, or x and y. The important thing is using the correct area formula: Area = side₁ × side₂.

Rectangle Area Formula with Given Dimensions

The area of the rectangle below is equal to 84.

AC = 7

What is the length of side AB?

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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) times length(AC)

00:08 Substitute in the relevant values into the formula according to the given data and proceed to solve for AB

00:14 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 84.

AC = 7

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:

$S=AB\times AC$

$84=AB\times7$

Let's now divide both sides by 7:

$AB=12$

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: 84 = AB × 7, then divide both sides
Check: Verify: 12 × 7 = 84 square units ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't add AB + 7 = 84 and solve for AB = 77! Addition gives perimeter, not area. Area requires multiplication. Always use A = length × width for rectangle area problems.

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

Why do I multiply the sides instead of adding them?

Area measures how much space is inside the rectangle, which requires multiplication. Adding gives you perimeter (distance around the outside). Think of area as counting squares: 12 rows of 7 squares each!

Which side is length and which is width?

It doesn't matter! In rectangles, you can call either side the length or width. The area formula A = l × w works the same way regardless of which dimension you call which.

How do I solve AB × 7 = 84?

Divide both sides by 7: $\frac{AB \times 7}{7} = \frac{84}{7}$ . The 7s cancel on the left, giving you AB = 12.

What if I get a decimal or fraction answer?

That's perfectly normal! Rectangle dimensions can be any positive number. Just make sure to check your work by multiplying your answer by the given dimension to see if you get the original area.

Can I use different letters instead of AB and AC?

Yes! The letters are just labels for the sides. You might see l and w for length and width, or x and y. The important thing is using the correct area formula: Area = side₁ × side₂.

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