Solve the Perimeter Equation: Finding X in a Trapezoid

Q: What exactly is the perimeter of a shape?

The perimeter is the total distance around the outside of any shape. For a trapezoid, you add up all four side lengths to get the perimeter.

Q: Why do I subtract instead of adding to find x?

You're using inverse operations! Since $ 30 + x = 36 $, you subtract 30 from both sides to isolate the variable x on one side.

Q: Does it matter which side is labeled as x?

No, it doesn't matter! Any unknown side can be called x. The perimeter formula works the same way regardless of which side you're solving for.

Q: How can I check if my perimeter calculation is right?

Add up all four sides using your answer: $ 13 + 12 + 5 + 6 = 36 $. If this equals the given perimeter, you're correct!

Q: What if the trapezoid had different side lengths?

The same method works for any trapezoid! Just substitute the different values into $ P = a + b + c + d $ and solve for the unknown.

Perimeter Equations with Unknown Side Lengths

Calculate X in the trapezoid below.

Perimeter = P

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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.

Perimeter = P

Step-by-step solution

To solve this problem, we'll utilize the formula for the perimeter of a trapezoid.

The formula for the perimeter is given by:

$P = a + b + c + d$

From the problem, we know:

The perimeter $P$ is 36.
The side lengths are 13, 12, and 5, with the unknown side as $x$ .

Plug these into the formula:

$36 = 13 + 12 + 5 + x$

Combine the known side lengths:

$36 = 30 + x$

To isolate $x$ , subtract 30 from both sides:

$x = 36 - 30$

Calculate the result:

$x = 6$

Therefore, the length of the missing side $x$ is 6.

Thus, the correct answer is choice 2, corresponding to $x = 6$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals sum of all four sides
Technique: Add known sides: 13 + 12 + 5 = 30
Check: Verify total: 6 + 13 + 12 + 5 = 36 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include all four sides in perimeter calculation
Don't calculate perimeter using only three sides = incomplete equation! This misses one side length and gives wrong totals. Always identify and include all four sides of the trapezoid in your perimeter formula.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

What exactly is the perimeter of a shape?

The perimeter is the total distance around the outside of any shape. For a trapezoid, you add up all four side lengths to get the perimeter.

Why do I subtract instead of adding to find x?

You're using inverse operations! Since $30 + x = 36$ , you subtract 30 from both sides to isolate the variable x on one side.

Does it matter which side is labeled as x?

No, it doesn't matter! Any unknown side can be called x. The perimeter formula works the same way regardless of which side you're solving for.

How can I check if my perimeter calculation is right?

Add up all four sides using your answer: $13 + 12 + 5 + 6 = 36$ . If this equals the given perimeter, you're correct!

What if the trapezoid had different side lengths?

The same method works for any trapezoid! Just substitute the different values into $P = a + b + c + d$ and solve for the unknown.

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