To solve this problem, we are dealing with two similar trapezoids, ABCD and WXYZ. Since they are similar, the corresponding sides are proportional.

Given:

• In trapezoid ABCD:

  • $AB = 35$ inches
  • $CD = 60$ inches

• In trapezoid WXYZ:

  • $WX = 7$ inches
  • $XY = 12$ inches
  • $WZ = 12$ inches
  • $ZY = 12$ inches

Since trapezoids ABCD and WXYZ are similar, the ratio of the corresponding sides should be the same. Therefore, we can set up the proportion between the corresponding sides $AB$ and $WX$, as well as $CD$ and $WZ$:

$\frac{AB}{WX} = \frac{CD}{WZ}$

Substituting the values we know:

$\frac{35}{7} = \frac{60}{w}$

Now solve for $w$ by cross-multiplying:

$35 \times w = 7 \times 60$ $35w = 420$ $w = \frac{420}{35} = 12$

Thus, the value of $w$ is 12 inches.

Let me know if you need further explanation or have additional questions!

Here are some follow-up questions:

1. How do you identify similar trapezoids from their properties?
2. What is the general formula for calculating the perimeter of a trapezoid?
3. How do the angles of similar trapezoids relate to each other?
4. Can this method be used for other polygons? How?
5. How would the solution change if the trapezoids were not similar?

Tip: When working with similar figures, always ensure that the corresponding sides are proportional!