Calculate X: Finding Rectangle Dimensions When Area = 72 and Length = 2X

Q: Why do I multiply X and 2X instead of adding them?

Because area is calculated by multiplying length × width, not adding them! When you add dimensions, you get part of the perimeter instead.

Q: How do I solve X² = 36?

Take the square root of both sides: $ \sqrt{X^2} = \sqrt{36} $. This gives you X = 6. Since we're measuring length, we only use the positive solution.

Q: What if I get 2X² = 72 but don't know what to do next?

Divide both sides by 2 first! This simplifies to $ X^2 = 36 $, making it much easier to solve by taking the square root.

Q: How can I check if X = 6 is correct?

Substitute back: If X = 6, then length = 2X = 12. Check: Area = 6 × 12 = 72 ✓ This matches the given area!

Q: Why don't we consider X = -6 as a solution?

While mathematically $ (-6)^2 = 36 $, lengths in geometry must be positive. A rectangle cannot have negative dimensions!

Rectangle Area with Variable Dimensions

The area of the rectangle below is equal to 72.

AC = X

AB = 2X

Calculate X.

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Step-by-step written solution

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Understand the problem

The area of the rectangle below is equal to 72.

AC = X

AB = 2X

Calculate X.

Step-by-step solution

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

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

$72=x\times2x$

$72=2x^2$

Let's proceed to simplify both sides of the equation by the HCF (highest common factor ) in this case 2:

$36=x^2$

Finally we remove the square root in order to solve the equation as follows:

$x=6$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area of rectangle equals length times width
Technique: Substitute variables: 72 = X × 2X = 2X²
Check: Verify X = 6: Area = 6 × 12 = 72 ✓

Common Mistakes

Avoid these frequent errors

Setting up the equation incorrectly with dimensions
Don't write 72 = X + 2X = 3X! This adds dimensions instead of multiplying them. Addition gives perimeter, not area. Always multiply length times width: 72 = X × 2X.

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 X and 2X instead of adding them?

Because area is calculated by multiplying length × width, not adding them! When you add dimensions, you get part of the perimeter instead.

How do I solve X² = 36?

Take the square root of both sides: $\sqrt{X^2} = \sqrt{36}$ . This gives you X = 6. Since we're measuring length, we only use the positive solution.

What if I get 2X² = 72 but don't know what to do next?

Divide both sides by 2 first! This simplifies to $X^2 = 36$ , making it much easier to solve by taking the square root.

How can I check if X = 6 is correct?

Substitute back: If X = 6, then length = 2X = 12. Check: Area = 6 × 12 = 72 ✓ This matches the given area!

Why don't we consider X = -6 as a solution?

While mathematically $(-6)^2 = 36$ , lengths in geometry must be positive. A rectangle cannot have negative dimensions!

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