Compare Trapezoids: Are Two Trapezoids with Sides x and x+16 Congruent?

Given the trapezoids in the drawing.

Are they the same trapezoid?

CCCxx+1610677

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are the trapezoids equal?
00:03 Let's mark trapezoids 1,2
00:06 The perimeter of a trapezoid equals the sum of its sides
00:10 Let's calculate the perimeter of trapezoid 1
00:21 This is the perimeter of trapezoid 1
00:24 Let's use the same method to calculate the perimeter of trapezoid 2
00:39 This is the size of trapezoid 2's perimeter and it equals trapezoid 1
00:46 The trapezoids have equal perimeter
00:50 But they are different because trapezoid 2 is right-angled
00:55 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Given the trapezoids in the drawing.

Are they the same trapezoid?

CCCxx+1610677

2

Step-by-step solution

We calculate the perimeter of the left trapezoid:

P=6+10+7+52x+5 P=6+10+7+\frac{5}{2}x+5

P=28+52x P=28+\frac{5}{2}x

We calculate the perimeter of the right trapezoid:

P=7+x+x+16+x2+5 P=7+x+x+16+\frac{x}{2}+5

P=212x+28 P=2\frac{1}{2}x+28

P=52x+28 P=\frac{5}{2}x+28

The perimeters of the two trapezoids are equal to each other.

3

Final Answer

No, but their perimeter is identical.

Practice Quiz

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Calculate the perimeter of the trapezoid below:

101010111111555101010

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