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

Question

Given the trapezoids in the drawing.

Are they the same trapezoid?

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

We calculate the perimeter of the left trapezoid:

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

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

We calculate the perimeter of the right trapezoid:

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

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

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

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

No, but their perimeter is identical.