Rectangle Area Problem: Finding BC When AB = 5cm and Area = 30cm²

Q: How do I know which side is which in the rectangle?

Look at the diagram carefully! The problem states AB = 5 cm, so identify points A and B on the rectangle. The side you're finding (BC) connects points B and C.

Q: Why do I multiply the sides together?

The area of a rectangle is always length × width. Since you know one side (5 cm) and the total area (30 cm²), multiplying gives you the equation to solve.

Q: What if I get a decimal or fraction answer?

That's completely normal! Rectangle problems can have any positive number as an answer. Just make sure your calculation is correct and the units match.

Q: How can I check if my answer makes sense?

Ask yourself: Does 5 × 6 = 30? Also check that your answer is reasonable - if one side is 5 cm and area is 30 cm², the other side should be around 6 cm.

Q: Do I need to worry about which side is length vs width?

No! For area calculations, it doesn't matter which side you call length or width. The formula A = l × w works the same either way.

Rectangle Area with Given Side Length

Below is the rectangle ABCD, which has an area of 30 cm².

Side AB is equal to 5 cm.
What is the length of side BC?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the length of side B C in this rectangle.

00:14 To solve this, we'll use the area formula for a rectangle, which is length times width.

00:20 We multiply side A B by side B C to get the area.

00:24 To make this easier, let's call the unknown side B C 'x'.

00:29 Now, we can put our known values into the formula and solve for x, step by step.

00:35 And there we have it! That's how we find the length of side B C.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is the rectangle ABCD, which has an area of 30 cm².

Side AB is equal to 5 cm.
What is the length of side BC?

Step-by-step solution

First, we will multiply side AB by side BC.

We know that side BC equals 5, therefore:

$AB\times BC=AB\times5$

We will label side AB as $x$ .

Therefore:

$5x=30$

Next, we will divide both sides by 5 to obtain the following:

$x=6$

Therefore:
$BC=6$

Final Answer

6 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width (A = l × w)
Technique: Set up equation 5 × BC = 30, then solve for BC
Check: Verify 5 cm × 6 cm = 30 cm² matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing which side to label as unknown
Don't assume the longer side is always unknown or mix up AB and BC = wrong setup! Students often label the wrong side as x, leading to incorrect equations. Always identify which measurement you're given and which you need to find before setting up your equation.

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

How do I know which side is which in the rectangle?

Look at the diagram carefully! The problem states AB = 5 cm, so identify points A and B on the rectangle. The side you're finding (BC) connects points B and C.

Why do I multiply the sides together?

The area of a rectangle is always length × width. Since you know one side (5 cm) and the total area (30 cm²), multiplying gives you the equation to solve.

What if I get a decimal or fraction answer?

That's completely normal! Rectangle problems can have any positive number as an answer. Just make sure your calculation is correct and the units match.

How can I check if my answer makes sense?

Ask yourself: Does 5 × 6 = 30? Also check that your answer is reasonable - if one side is 5 cm and area is 30 cm², the other side should be around 6 cm.

Do I need to worry about which side is length vs width?

No! For area calculations, it doesn't matter which side you call length or width. The formula A = l × w works the same either way.

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Rectangle Area Problem: Finding BC When AB = 5cm and Area = 30cm²

Rectangle Area with Given Side Length

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which side is which in the rectangle?

Why do I multiply the sides together?

What if I get a decimal or fraction answer?

How can I check if my answer makes sense?

Do I need to worry about which side is length vs width?

🌟 Unlock Your Math Potential

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