Rectangle Perimeter Problem: Finding X When Perimeter = 28 and Width = 11

Rectangle Perimeter with Variable Dimensions

The perimeter of the rectangle below is 28.

Calculate the value of x.

AAABBBCCCDDDx11

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 Opposite sides are equal in a rectangle
00:17 The perimeter of the rectangle equals the sum of its sides
00:26 Substitute appropriate values and solve for X
00:47 Collect like terms
01:01 Isolate X
01:16 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The perimeter of the rectangle below is 28.

Calculate the value of x.

AAABBBCCCDDDx11

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information
  • Step 2: Use the perimeter formula
  • Step 3: Solve for x x

Now, let's work through each step:

Step 1: The problem gives us that the perimeter of the rectangle is 28, one side (length) is 11, and the other side (width) is x x .
Step 2: We'll use the formula for the perimeter of a rectangle: P=2(l+w) P = 2(l + w) . In this problem, l=11 l = 11 and w=x w = x so:

28=2(11+x) 28 = 2(11 + x)

Step 3: Divide both sides by 2 to isolate the expression inside the parentheses:

14=11+x 14 = 11 + x

Step 4: Subtract 11 from both sides to solve for x x :

x=1411=3 x = 14 - 11 = 3

Therefore, the value of x x is 3 3 .

3

Final Answer

3

Key Points to Remember

Essential concepts to master this topic
  • Formula: Rectangle perimeter equals two times length plus width
  • Technique: Substitute known values: 28=2(11+x) 28 = 2(11 + x)
  • Check: Verify answer: 2(11+3)=2(14)=28 2(11 + 3) = 2(14) = 28

Common Mistakes

Avoid these frequent errors
  • Forgetting to multiply both dimensions by 2
    Don't use P = l + w + l + w = 11 + x + 11 + x = 28! While this gives the same answer here, it's inefficient and error-prone. Always use the standard formula P = 2(l + w) to avoid calculation mistakes.

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?

1.51.51.5AAABBBCCCDDD9.5

FAQ

Everything you need to know about this question

Which side is the length and which is the width?

+

It doesn't matter! In this problem, whether you call 11 the length or width, x will still equal 3. The perimeter formula works the same way regardless of which dimension you label as length or width.

Why do we multiply by 2 in the perimeter formula?

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Because a rectangle has 4 sides: 2 lengths and 2 widths. Instead of adding all four sides separately, we use P=2(l+w) P = 2(l + w) as a shortcut to multiply the sum by 2.

What if I get a negative number for x?

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Check your arithmetic! In geometry problems, dimensions are always positive numbers. If you get negative, you likely made a calculation error somewhere.

Can I solve this by guessing and checking?

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You could, but it's not efficient! Using the algebraic method gives you the exact answer in just a few steps, and it works for any numbers - not just simple ones.

How do I know when to divide by 2?

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After substituting into 28=2(11+x) 28 = 2(11 + x) , you need to isolate what's in parentheses. Since it's multiplied by 2, you divide both sides by 2 to undo that operation.

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