Find X in Rectangle: Area 40 cm² with Side Length 2x+4

Rectangle Area with Algebraic Expression

Rectangle ABCD has an area of

40 cm².

Side BC is equal to 5 cm.
Work out the value of x.
S=40S=40S=402x+42x+42x+4555AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:13 Let's find the value of X.
00:16 First, we'll use the formula for the area of a rectangle.
00:20 Multiply side A-B by side B-C.
00:24 Now, plug in the numbers and solve for X.
00:29 Be sure to open the parentheses carefully.
00:35 Next, let's isolate X.
00:39 And there you go, that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Rectangle ABCD has an area of

40 cm².

Side BC is equal to 5 cm.
Work out the value of x.
S=40S=40S=402x+42x+42x+4555AAABBBCCCDDD

2

Step-by-step solution

Let's multiply side AB by side BC

We'll set up the data as follows:

5(2x+4)=40 5(2x+4)=40

Let's multiply 5 by each term in parentheses:

10x+20=40 10x+20=40

We'll move 20 to the right side and change its sign accordingly:

10x=4020 10x=40-20

Now we get:

10x=20 10x=20

Let's divide both sides by 10:

x=2 x=2

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Length × Width = Area for rectangles
  • Technique: Set up equation 5(2x+4)=40 5(2x+4) = 40 using given measurements
  • Check: Substitute x = 2: 5(2(2)+4)=5(8)=40 5(2(2)+4) = 5(8) = 40

Common Mistakes

Avoid these frequent errors
  • Forgetting to use parentheses when multiplying
    Don't write 5 × 2x + 4 = 40 instead of 5(2x + 4) = 40! Without parentheses, you only multiply 5 by 2x, not the entire expression 2x + 4. Always use parentheses to show that 5 multiplies the whole expression.

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?
666444AAABBBCCCDDD

FAQ

Everything you need to know about this question

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

+

It doesn't matter! For rectangles, area = length × width works the same regardless of which side you call length or width. Just multiply the two given measurements.

Why do I need to distribute the 5 to both terms?

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When you have 5(2x+4) 5(2x+4) , the 5 must multiply everything inside the parentheses. This gives you 5×2x+5×4=10x+20 5 \times 2x + 5 \times 4 = 10x + 20 .

What if I get a negative answer for x?

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Check your work! In this problem, x represents part of a length measurement, so it should be positive. A negative x would mean a negative length, which doesn't make sense.

Can I solve this without distributing first?

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Yes! You could divide both sides by 5 first: 2x+4=8 2x + 4 = 8 , then solve. Both methods work, so use whichever feels easier to you.

How do I verify my final answer?

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Substitute x = 2 back into the original measurements: Side AB = 2(2)+4=8 2(2) + 4 = 8 cm, Side BC = 5 cm. Check: 8×5=40 8 \times 5 = 40 cm² ✓

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