Rectangle Area Problem: Finding Side Length AB When Area = 63 and AC = 7

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

Area measures the space inside a rectangle, which requires multiplication. Adding sides gives you perimeter (the distance around), not area!

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

It doesn't matter! Rectangle area is commutative, meaning AB × AC = AC × AB. Just multiply the two perpendicular sides together.

Q: What if I get a decimal or fraction for the side length?

That's completely normal! Real-world rectangles often have non-whole number dimensions. Just make sure your calculation gives the correct area when you check.

Q: Can I use this method for squares too?

Absolutely! A square is a special rectangle where all sides are equal. Use $ s^2 = \text{Area} $, so $ s = \sqrt{\text{Area}} $.

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

Ask yourself: Does this make sense? If AC = 7 and area = 63, then AB should be around 9 because 7 × 9 ≈ 63. Always do a quick mental estimate!

Rectangle Area Formula with Given Side

The area of the rectangle below is equal to 63.

AC = 7

How long is 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) multiplied by length(AC)

00:07 Substitute the relevant values into the formula according to the given data and proceed to solve for AB

00:11 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 63.

AC = 7

How long is side AB?

Step-by-step solution

We use the formula to calculate a rectangle: length times width:

$AB\times AC=S$

We place the existing data into the formula:

$AB\times7=63$

$7AB=63$

We divide both sides by 7:

$AB=9$

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: AB × 7 = 63, so AB = 9
Check: Verify by multiplying: 9 × 7 = 63 square units ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate AB + AC = 63 to get AB = 56! Addition gives perimeter, not area. Always multiply length times width for rectangle area calculations.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do we multiply the sides instead of adding them?

Area measures the space inside a rectangle, which requires multiplication. Adding sides gives you perimeter (the distance around), not area!

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

It doesn't matter! Rectangle area is commutative, meaning AB × AC = AC × AB. Just multiply the two perpendicular sides together.

What if I get a decimal or fraction for the side length?

That's completely normal! Real-world rectangles often have non-whole number dimensions. Just make sure your calculation gives the correct area when you check.

Can I use this method for squares too?

Absolutely! A square is a special rectangle where all sides are equal. Use $s^2 = \text{Area}$ , so $s = \sqrt{\text{Area}}$ .

How do I check if my answer is reasonable?

Ask yourself: Does this make sense? If AC = 7 and area = 63, then AB should be around 9 because 7 × 9 ≈ 63. Always do a quick mental estimate!

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