Solve for X: Rectangle Area 27 with Side Length 3X

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

Area measures the space inside the rectangle, which requires multiplying length × width. Adding gives you the perimeter (distance around the rectangle), which is totally different!

Q: What does 3X mean in this problem?

The 3X means 3 times X, so if X = 3, then 3X = 3 × 3 = 9. The side AB has length 9 when X = 3.

Q: How do I solve 27 = 9x?

Divide both sides by 9: $ \frac{27}{9} = \frac{9x}{9} $. This gives you x = 3 because 27 ÷ 9 = 3.

Rectangle Areas with Variable Side Lengths

The area of the rectangle is equal to 27.

AC = 3

AB = 3X

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the value of X. Are you ready?

00:12 To calculate the area of a rectangle, multiply the width, A B, by the length, A C.

00:18 Now, substitute the given numbers into the formula and solve for X.

00:23 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the rectangle is equal to 27.

AC = 3

AB = 3X

Calculate X.

Step-by-step solution

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

Let's insert the known data into the formula:

$27=3\times3x$

$27=9x$

Lastly let's divide both sides by 9:

$x=3$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width (A = l × w)
Technique: Set up equation 27 = 3 × 3x, then simplify to 27 = 9x
Check: Substitute x = 3: Area = 3 × (3×3) = 3 × 9 = 27 ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't add AC + AB = 3 + 3x to find area = wrong formula! Addition gives perimeter, not area, leading to completely incorrect answers. Always multiply length × width for rectangle area.

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 the rectangle, which requires multiplying length × width. Adding gives you the perimeter (distance around the rectangle), which is totally different!

What does 3X mean in this problem?

The 3X means 3 times X, so if X = 3, then 3X = 3 × 3 = 9. The side AB has length 9 when X = 3.

How do I solve 27 = 9x?

Divide both sides by 9: $\frac{27}{9} = \frac{9x}{9}$ . This gives you x = 3 because 27 ÷ 9 = 3.

Can I check my answer a different way?

Yes! Calculate the actual dimensions: AC = 3 and AB = 3×3 = 9. Then verify: 3 × 9 = 27 ✓. The area matches!

What if I get a fraction for X?

That's totally normal! Many problems have fractional answers. Just make sure to substitute back carefully when checking your work.

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