Solve for X in a Trapezoid: Perimeter = 30.3 with Side 12x

Q: Why do we need to combine 12x and x together?

Both 12x and x contain the same variable, so they're called like terms. You can add them: 12x + x = 13x, just like 12 apples + 1 apple = 13 apples!

Q: What if I get a decimal answer instead of a whole number?

That's completely normal! Many real-world problems have decimal solutions. The key is to check your work by substituting back into the original equation.

Q: Can I solve this without combining like terms first?

You could, but it's much harder! Combining like terms simplifies $ 12x + 8.7 + x + 2.4 = 30.3 $ to $ 13x + 11.1 = 30.3 $, making the algebra much easier.

Q: How do I check if x = 1.477 is really correct?

Substitute back: $ 12(1.477) + 8.7 + 1.477 + 2.4 $. Calculate: $ 17.724 + 8.7 + 1.477 + 2.4 = 30.301 \approx 30.3 $ ✓

Perimeter Equations with Variable Expressions

Calculate x in the trapezoid below.

P = Perimeter

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate x in the trapezoid below.

P = Perimeter

Step-by-step solution

To find $x$ in the trapezoid with a given perimeter $P = 30.3$ , we follow these steps:

Step 1: Write the perimeter equation using all sides: $12x + 8.7 + x + 2.4 = 30.3$ .
Step 2: Combine like terms: $13x + 11.1 = 30.3$ .
Step 3: Isolate $x$ by subtracting 11.1 from both sides: $13x = 19.2$ .
Step 4: Solve for $x$ by dividing both sides by 13: $x = \frac{19.2}{13} \approx 1.477$ .

Therefore, the solution to the problem is $x = 1.477$ .

Final Answer

1.477

Key Points to Remember

Essential concepts to master this topic

Perimeter Rule: Add all four sides of the trapezoid together
Technique: Combine like terms: 12x + x = 13x before solving
Check: Substitute x = 1.477: 12(1.477) + 8.7 + 1.477 + 2.4 = 30.3 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add all four sides in perimeter equation
Don't just add the sides with variables and ignore the constant sides = incomplete equation! This gives you the wrong perimeter total and leads to incorrect solutions. Always add every single side shown in the figure: 12x + 8.7 + x + 2.4.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the trapezoid according to the following data:

FAQ

Everything you need to know about this question

Why do we need to combine 12x and x together?

Both 12x and x contain the same variable, so they're called like terms. You can add them: 12x + x = 13x, just like 12 apples + 1 apple = 13 apples!

How do I know which sides to add for the perimeter?

Look at the trapezoid diagram carefully. The perimeter includes all four sides: the top (12x), right side (8.7), bottom (x), and left side (2.4). Don't miss any!

What if I get a decimal answer instead of a whole number?

That's completely normal! Many real-world problems have decimal solutions. The key is to check your work by substituting back into the original equation.

Can I solve this without combining like terms first?

You could, but it's much harder! Combining like terms simplifies $12x + 8.7 + x + 2.4 = 30.3$ to $13x + 11.1 = 30.3$ , making the algebra much easier.

How do I check if x = 1.477 is really correct?

Substitute back: $12(1.477) + 8.7 + 1.477 + 2.4$ . Calculate: $17.724 + 8.7 + 1.477 + 2.4 = 30.301 \approx 30.3$ ✓

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