Trapezoid Perimeter: Express in Terms of 5X, 3X, Z, and 3Y

Variable Expression Addition with Algebraic Terms

Look at the trapezoid in the figure.

Express the perimeter of the trapezoid using the given variables.

5X5X5X3X3X3XZZZ3Y3Y3Y

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perimeter of the trapezoid
00:04 The perimeter of the trapezoid equals the sum of its sides
00:15 Let's substitute appropriate values and solve for the perimeter
00:34 Let's collect all possible factors
00:38 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

Look at the trapezoid in the figure.

Express the perimeter of the trapezoid using the given variables.

5X5X5X3X3X3XZZZ3Y3Y3Y

2

Step-by-step solution

To solve this problem, we'll express the perimeter of the trapezoid by summing up its side lengths:

  • Step 1: Identify the given side lengths.

  • Step 2: Apply the perimeter formula for the trapezoid.

  • Step 3: Simplify the resulting expression.

Let's work through these steps:

Step 1: The trapezoid has the following side lengths:
- Top base: 5X5X
- Left side: 3X3X
- Bottom base: ZZ
- Right side: 3Y3Y

Step 2: Apply the perimeter formula:
The perimeter P P is given by the sum of all sides:
\begin{equation} P=5X+3X+Z+3Y P = 5X + 3X + Z + 3Y

Step 3: Simplify the expression:
Combine like terms:
P=(5X+3X)+Z+3Y=8X+3Y+Z P = (5X + 3X) + Z + 3Y = 8X + 3Y + Z

Therefore, the perimeter of the trapezoid is expressed as 8X+3Y+Z 8X + 3Y + Z .

3

Final Answer

8X+3Y+Z

Key Points to Remember

Essential concepts to master this topic
  • Perimeter Formula: Add all four sides of the trapezoid together
  • Technique: Combine like terms: 5X + 3X = 8X
  • Check: Count all four sides in final expression: 8X + 3Y + Z ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying variables instead of adding them
    Don't multiply 5X × 3X × Z × 3Y = 45X²YZ! Perimeter means adding lengths, not multiplying them. Always add each side length: 5X + 3X + Z + 3Y = 8X + 3Y + Z.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

FAQ

Everything you need to know about this question

Why do I combine 5X and 3X but not the other terms?

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Like terms have the same variable and exponent! Since 5X and 3X both have just 'X', you can add them: 5X + 3X = 8X. But Z and 3Y have different variables, so they stay separate.

What if I wrote the answer as Z + 8X + 3Y instead?

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That's mathematically correct! Addition is commutative, meaning order doesn't change the result. However, it's conventional to write terms in alphabetical order or with like terms grouped together.

How do I know this is a trapezoid from the diagram?

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A trapezoid has exactly one pair of parallel sides. In the diagram, you can see the top and bottom sides are horizontal (parallel), while the left and right sides are slanted and not parallel to each other.

Can I simplify 8X + 3Y + Z any further?

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No, this expression is fully simplified! Since 8X, 3Y, and Z all have different variables or coefficients, there are no more like terms to combine.

What does perimeter mean in geometry?

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Perimeter is the total distance around the outside of a shape. Think of it like walking around the edge - you'd travel along each side exactly once, so you add all the side lengths together.

Why don't I need to know the actual measurements?

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The problem asks for an algebraic expression using the given variables. This means we express the perimeter in terms of X, Y, and Z rather than finding a specific number value.

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