Find X When Two Trapezoids Have Equal Perimeters: 5X + 2X-2 + 6X Solution

Q: How do I know which sides belong to which trapezoid?

Look at the diagram carefully! The first trapezoid has sides labeled 5X, (2X-2), 6X, and (X-1). The second trapezoid has sides (2X+1), 4X, 3X, and (4X+1).

Q: Why do I set the perimeters equal to each other?

The problem states that the perimeters are equal. This means whatever the first trapezoid's perimeter equals, the second trapezoid's perimeter must equal the same value!

Q: What if I get confused combining like terms?

Take it step by step! For the first trapezoid: 5X + 2X + X + 6X = 14X, then -2 + (-1) = -3. So you get 14X - 3.

Q: How can I check if X = 5 is really correct?

Substitute X = 5 into both perimeter expressions:First trapezoid: 14(5) - 3 = 70 - 3 = 67Second trapezoid: 13(5) + 2 = 65 + 2 = 67Since both equal 67, X = 5 is correct!

Q: What does it mean when two shapes have equal perimeters?

It means both shapes have the same total distance around their edges. Even though the trapezoids look different, when you walk around the complete boundary of each one, you travel the same total distance!

Perimeter Equations with Variable Expressions

Calculate X given that the perimeters of the two trapezoids are equal.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 The perimeter of the trapezoid equals the sum of its sides

00:07 Let's substitute appropriate values according to the given data and solve for the perimeter

00:18 Let's gather all possible factors

00:31 This is the perimeter size of trapezoid 1

00:36 Now let's use the same method to find the perimeter of trapezoid 2

00:49 Let's gather all possible factors

00:58 This is the perimeter size of trapezoid 2

01:01 The perimeters of the trapezoids are equal according to the given data

01:05 Now let's compare the perimeters and solve for X

01:10 Let's move X to the left side and numbers to the right side of the equation

01:21 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate X given that the perimeters of the two trapezoids are equal.

Step-by-step solution

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

Step 1: Calculate the perimeter of each trapezoid
Step 2: Set the perimeters equal to each other
Step 3: Solve for $X$

Let's work through the steps:

Step 1: Calculate the perimeter of each trapezoid.

For the first trapezoid, the perimeter is:

$5X + (2X - 2) + (X - 1) + 6X = 14X - 3$

For the second trapezoid, the perimeter is:

$(2X + 1) + 4X + (4X + 1) + 3X = 13X + 2$

Step 2: Set the two perimeter expressions equal:

$14X - 3 = 13X + 2$

Step 3: Solve for $X$ .

Subtract $13X$ from both sides:

$X - 3 = 2$

Add 3 to both sides:

$X = 5$

Therefore, the solution to the problem is $X = 5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Perimeter Rule: Add all four sides of each trapezoid together
Technique: Combine like terms: 5X + (2X-2) + (X-1) + 6X = 14X - 3
Check: Substitute X = 5: both perimeters equal 67 units ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include all four sides when calculating perimeter
Don't just add the labeled sides you can see clearly = incomplete perimeter! Missing even one side gives a completely wrong equation to solve. Always identify and include all four sides of each trapezoid in your perimeter calculation.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

How do I know which sides belong to which trapezoid?

Look at the diagram carefully! The first trapezoid has sides labeled 5X, (2X-2), 6X, and (X-1). The second trapezoid has sides (2X+1), 4X, 3X, and (4X+1).

Why do I set the perimeters equal to each other?

The problem states that the perimeters are equal. This means whatever the first trapezoid's perimeter equals, the second trapezoid's perimeter must equal the same value!

What if I get confused combining like terms?

Take it step by step! For the first trapezoid: 5X + 2X + X + 6X = 14X, then -2 + (-1) = -3. So you get 14X - 3.

How can I check if X = 5 is really correct?

Substitute X = 5 into both perimeter expressions:

First trapezoid: 14(5) - 3 = 70 - 3 = 67
Second trapezoid: 13(5) + 2 = 65 + 2 = 67

Since both equal 67, X = 5 is correct!

What does it mean when two shapes have equal perimeters?

It means both shapes have the same total distance around their edges. Even though the trapezoids look different, when you walk around the complete boundary of each one, you travel the same total distance!

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