Calculate Trapezoid Perimeter When X=3: Variable Side Length Problem

Q: Do I need to substitute x in every single expression?

Yes, absolutely! When x=3, you must replace every x with 3. So x becomes 3, (x+1) becomes (3+1)=4, and (6+x) becomes (6+3)=9.

Q: What if I forget to add all four sides?

A trapezoid has 4 sides, so you need all 4 measurements! From the diagram: top side (10), left side (x), bottom side (6+x), and right side (x+1).

Q: Can I simplify the expressions first before substituting?

You could combine like terms first: $ 10 + x + (6+x) + (x+1) = 17 + 3x $, then substitute x=3 to get $ 17 + 3(3) = 17 + 9 = 26 $. Both methods work!

Variable Substitution with Algebraic Expressions

If X=3

Calculate the perimeter of the trapezoid

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Step-by-step video solution

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Understand the problem

If X=3

Calculate the perimeter of the trapezoid

Step-by-step solution

To calculate the perimeter, we add up all the sides:

$10+x+(6+x)+(x+1)$

Now, given that x equals 3, we substitute in the appropriate places:

$10+3+(6+3)+(3+1)=$

$10+3+9+4=$

$13+13=26$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: Add all four sides of the trapezoid together
Substitution: Replace x with 3 in each expression: x becomes 3, x+1 becomes 4
Verification: Check that 10+3+9+4=26 by adding step by step ✓

Common Mistakes

Avoid these frequent errors

Substituting x incorrectly in compound expressions
Don't substitute x=3 only in simple x terms and forget compound expressions like (6+x) = wrong partial substitution! This leads to mixing variables with numbers. Always substitute x=3 in every single expression: x becomes 3, (x+1) becomes (3+1)=4, and (6+x) becomes (6+3)=9.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

Do I need to substitute x in every single expression?

Yes, absolutely! When x=3, you must replace every x with 3. So x becomes 3, (x+1) becomes (3+1)=4, and (6+x) becomes (6+3)=9.

What if I forget to add all four sides?

A trapezoid has 4 sides, so you need all 4 measurements! From the diagram: top side (10), left side (x), bottom side (6+x), and right side (x+1).

Can I simplify the expressions first before substituting?

You could combine like terms first: $10 + x + (6+x) + (x+1) = 17 + 3x$ , then substitute x=3 to get $17 + 3(3) = 17 + 9 = 26$ . Both methods work!

How do I know which sides correspond to which expressions?

Look at the diagram carefully! Each side is labeled with its length. The top side is 10, left side is x, bottom side is 6+x, and right side is x+1.

What if I get a different answer when I check my work?

Go back and check your substitution step by step. Make sure you replaced every x with 3 and added all four sides correctly: 10 + 3 + 9 + 4.

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