Trapezoid Perimeter Problem: Finding Missing Base Length in 34cm Figure

Trapezoid Perimeter with Impossible Dimensions

The perimeter of the trapezoid in the drawing is 34 cm. What is the length of the missing base?

121212141414101010

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find side AB
00:04 The perimeter of the trapezoid equals the sum of its sides
00:13 Let's substitute appropriate values and solve for AB
00:31 Let's isolate AB
00:46 We got that the side length is less than 0, therefore it's impossible
00:50 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The perimeter of the trapezoid in the drawing is 34 cm. What is the length of the missing base?

121212141414101010

2

Step-by-step solution

To solve for the missing base of the trapezoid, follow these steps:

  • Identify given values: Perimeter P=34cm P = 34 \, \text{cm} , base 1 a=14cm a = 14 \, \text{cm} , leg 1 c=10cm c = 10 \, \text{cm} , leg 2 d=12cm d = 12 \, \text{cm} .
  • Set up the equation for the perimeter: P=a+b+c+d=34 P = a + b + c + d = 34 Substitute known values: 14+b+10+12=34 14 + b + 10 + 12 = 34
  • Simplify the equation: 36+b=34 36 + b = 34
  • Solve for b b : b=3436=2 b = 34 - 36 = -2

Since a side length cannot be negative, this trapezoid is impossible with these dimensions.

The correct choice is This trapeze is not possible.

3

Final Answer

This trapeze is not possible.

Key Points to Remember

Essential concepts to master this topic
  • Perimeter Formula: Add all four sides of the trapezoid together
  • Substitution: Replace known values: 14 + b + 10 + 12 = 34
  • Reality Check: Negative side length means the trapezoid cannot exist ✓

Common Mistakes

Avoid these frequent errors
  • Accepting negative side lengths as valid answers
    Don't solve b = -2 and choose '2 cm' as the answer! Negative lengths are impossible in geometry. Always check if your calculated side length is positive and makes geometric sense.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

FAQ

Everything you need to know about this question

Why can't a side length be negative?

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In geometry, length is always positive! A negative length like -2 cm has no physical meaning - you can't measure negative distance with a ruler.

What does it mean when a shape is 'impossible'?

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An impossible shape means the given measurements cannot form that shape in real life. The sides don't add up correctly to create the required perimeter.

How do I know when to look for impossible shapes?

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Always check your final answer for reasonableness! If you get negative lengths, zero lengths, or measurements that seem too large/small, the shape might be impossible.

Could I have made an arithmetic error instead?

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Good thinking! Always double-check your addition: 14 + 10 + 12 = 36. Since 36 > 34, we need b = 34 - 36 = -2, confirming the shape is impossible.

Are there other ways shapes can be impossible?

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Yes! Triangles with sides that don't satisfy the triangle inequality, or rectangles with negative width/height are also impossible. Always verify geometric constraints.

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