Calculate Trapezoid Perimeter: Solving with 3X+1, 3X-1, 2X+3, and 2X

Q: Why can't I just add all the numbers together?

Because variables and constants are different types! You can only combine terms that have the same variable part. Think of X as apples and numbers as oranges - you can't add them directly.

Q: What's the difference between 3X and 3?

3X means 3 times some unknown number X, while 3 is just the number 3. They're completely different mathematical objects that must be handled separately when adding.

Q: How do I know which terms to combine?

Look for like terms - terms with the same variable part. All X terms go together: $ 3X + 2X + 3X + 2X $. All constants go together: $ 1 + 3 - 1 + 0 $.

Q: What if I get confused with the signs?

Write out each term carefully with its sign: (+3X + 1) + (+2X + 3) + (+3X - 1) + (+2X). This helps you see which terms are positive and negative.

Algebraic Perimeter with Variable Expressions

Express the perimeter of the following trapezoid:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the perimeter of the trapezoid using X

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

00:15 Substitute appropriate values according to the given data and solve for the perimeter

00:41 Gather all possible factors

00:53 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Express the perimeter of the following trapezoid:

Step-by-step solution

To solve this problem, we will calculate the perimeter of the trapezoid using the expressions given for each side:

Top side length: $3X + 1$
Bottom side length: $2X + 3$
Right side length: $3X - 1$
Left side length: $2X$

The formula to find the perimeter $P$ of a trapezoid is to sum the lengths of all four sides:

$P = (3X + 1) + (2X + 3) + (3X - 1) + (2X)$

First, we will combine like terms:

Add up all the $X$ terms: $3X + 2X + 3X + 2X = 10X$
Add up the constant terms: $1 + 3 - 1 + 0 = 3$

Therefore, the perimeter of the trapezoid is:

$P = 10X + 3$

The correct choice is the option containing the expression $10X + 3$ .

Thus, the solution to the problem is $10X + 3$ .

Final Answer

$10x+3$

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals sum of all four side lengths
Technique: Combine like terms: 3X + 2X + 3X + 2X = 10X
Check: Count coefficients separately: X terms give 10X, constants give +3 ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients and constants together incorrectly
Don't combine 3X + 1 as 4X = wrong variable coefficient! This mixes variables with numbers, creating an impossible expression. Always keep X terms separate from constant terms when combining like terms.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

Why can't I just add all the numbers together?

Because variables and constants are different types! You can only combine terms that have the same variable part. Think of X as apples and numbers as oranges - you can't add them directly.

What's the difference between 3X and 3?

3X means 3 times some unknown number X, while 3 is just the number 3. They're completely different mathematical objects that must be handled separately when adding.

How do I know which terms to combine?

Look for like terms - terms with the same variable part. All X terms go together: $3X + 2X + 3X + 2X$ . All constants go together: $1 + 3 - 1 + 0$ .

What if I get confused with the signs?

Write out each term carefully with its sign: (+3X + 1) + (+2X + 3) + (+3X - 1) + (+2X). This helps you see which terms are positive and negative.

Can I check my answer somehow?

Yes! Pick any value for X (like X = 1) and calculate each side length, then add them up. Your algebraic answer should give the same result when you substitute that X value.

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