Rectangle Problem: Find Side BC When Area is 64 cm² and AB = 4BC

Q: Why do we write the equation as 4x² instead of just x × 4x?

Both are correct mathematically! Writing $ 4x^2 $ is just the simplified form of $ x \times 4x $. It makes the equation easier to solve.

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

In a rectangle, it doesn't matter! Area = length × width = width × length. The key is identifying the relationship: AB = 4BC means one side is 4 times the other.

Q: What if I get a negative answer when taking the square root?

Since we're measuring a physical side length, we only use the positive square root. Negative lengths don't make sense in geometry problems!

Area Formulas with Algebraic Variables

Given the rectangle ABCD

Given BC=X and the side AB is 4 timis larger than the side BC.

The area of the rectangle is 64 cm².

Calculate the side BC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate BC

00:04 The formula for calculating rectangle area is side(AB) multiplied by side (BC)

00:21 Let's substitute appropriate values and solve for X

00:32 Divide by 4

00:38 Extract the root to find X

00:45 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the rectangle ABCD

Given BC=X and the side AB is 4 timis larger than the side BC.

The area of the rectangle is 64 cm².

Calculate the side BC

Step-by-step solution

Let's begin by calculating the area of the rectangle using the given data:

$64=4x\times x$

$64=4x^2$

Next we will divide both sides by 4:

$16=x^2$

And we will remove the square root:

$4=x$

Therefore, BC equals 4.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width
Technique: Substitute relationships: $64 = 4x \times x = 4x^2$
Check: Verify BC = 4: Area = 4×16 = 64 cm² ✓

Common Mistakes

Avoid these frequent errors

Setting up the equation with incorrect side relationships
Don't write 64 = x × 4x as two separate unknowns = treating them as different variables! This ignores the given relationship that AB = 4BC. Always substitute the relationship first: if BC = x, then AB = 4x.

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 we write the equation as 4x² instead of just x × 4x?

Both are correct mathematically! Writing $4x^2$ is just the simplified form of $x \times 4x$ . It makes the equation easier to solve.

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

In a rectangle, it doesn't matter! Area = length × width = width × length. The key is identifying the relationship: AB = 4BC means one side is 4 times the other.

What if I get a negative answer when taking the square root?

Since we're measuring a physical side length, we only use the positive square root. Negative lengths don't make sense in geometry problems!

Can I solve this without using x as a variable?

You could try, but using a variable like x makes it much cleaner! It helps you organize the relationship between sides and set up the equation systematically.

How do I check if BC = 4 cm is really correct?

Substitute back into the area formula: If BC = 4, then AB = 4×4 = 16. Area = $16 \times 4 = 64$ cm². This matches the given area, so it's correct!

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