Find B2C2 Length: Comparing Trapezoids with Equal Perimeters of 5-7 Units

Q: Why can I cancel out X from both sides of the equation?

Since X appears on both sides with the same value, subtracting X from both sides maintains the equality. This is a fundamental property of equations - what you do to one side, you must do to the other!

Q: How do I know which sides correspond between the two trapezoids?

Look at the diagram carefully! Both trapezoids have a top side of 5 and a bottom side of 7. The side lengths X and the unknown B2C2 are the remaining sides we need to work with.

Q: What if the trapezoids had different orientations?

The orientation doesn't matter for perimeter problems! Whether a trapezoid is upright or rotated, the sum of all four sides remains the same.

Q: Can I solve this without setting up an equation?

While you might guess and check, setting up the equation guarantees the correct answer and shows your mathematical reasoning clearly. It's always the most reliable method!

Q: What if both trapezoids had two unknown sides?

You'd need additional information to solve the problem. With two unknowns, you typically need two equations or constraints to find unique solutions.

Perimeter Equations with Unknown Side Lengths

How long is B2C2 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

00:05 Let's find the length of side B two C two.

00:10 First, we'll calculate the perimeter of Trapezoid one. Let's begin!

00:15 Remember, the perimeter is just the sum of all sides.

00:19 Substitute the given values to find the perimeter of Trapezoid one.

00:24 That's the perimeter of Trapezoid one! Great job!

00:28 Now, let's use the same method to calculate the perimeter of Trapezoid two.

00:35 We can substitute the perimeter of Trapezoid one to solve for side B two C two.

00:45 Let's isolate side B two C two to find its length.

01:01 And there you have it! That's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

How long is B2C2 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 Trapezoid 1.
Step 2: Set the perimeters of the trapezoids equal to each other.
Step 3: Solve the equation for the unknown length $B2C2$ .

Now, let's work through each step:
Step 1: The perimeter of Trapezoid 1 is given by the sum: $P_1 = 5 + 6 + 7 + X = 18 + X$
Step 2: Assume the perimeter of Trapezoid 2 is the same: $P_2 = 5 + 7 + X + B2C2 = 12 + X + B2C2$
Step 3: Equate $P_1$ and $P_2$ : $18 + X = 12 + X + B2C2$ Subtract $X$ from both sides: $18 = 12 + B2C2$ Finally, solve for $B2C2$ : $B2C2 = 18 - 12 = 6$

Therefore, the solution to the problem is $B2C2 = 6$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Equal perimeters mean sum of all sides are equal
Technique: Set perimeter equations equal: 18 + X = 12 + X + B2C2
Check: Both trapezoids have perimeter 18 + X when B2C2 = 6 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include all four sides in perimeter calculation
Don't add only three sides like 5 + 6 + 7 = 18 and ignore the fourth side X! This gives an incomplete perimeter and wrong equation setup. Always include every single side when calculating perimeter, even the unknown ones.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why can I cancel out X from both sides of the equation?

Since X appears on both sides with the same value, subtracting X from both sides maintains the equality. This is a fundamental property of equations - what you do to one side, you must do to the other!

How do I know which sides correspond between the two trapezoids?

Look at the diagram carefully! Both trapezoids have a top side of 5 and a bottom side of 7. The side lengths X and the unknown B2C2 are the remaining sides we need to work with.

What if the trapezoids had different orientations?

The orientation doesn't matter for perimeter problems! Whether a trapezoid is upright or rotated, the sum of all four sides remains the same.

Can I solve this without setting up an equation?

While you might guess and check, setting up the equation guarantees the correct answer and shows your mathematical reasoning clearly. It's always the most reliable method!

What if both trapezoids had two unknown sides?

You'd need additional information to solve the problem. With two unknowns, you typically need two equations or constraints to find unique solutions.

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