https://file.aiquickdraw.com/mathbot/file/1725788219306c1sv9wdm.jpg

The image shows a right-angled trapezoid where you are tasked with finding the value of \( m \), which is the length of the diagonal in the trapezoid. From the given dimensions:

- One side of the trapezoid is 25 units.
- The other side is 50 units.
- The distance between the parallel sides (the height of the trapezoid) is 60 units.

We can apply the Pythagorean theorem here to solve for the value of \( m \), as the diagonal forms a right triangle with one of the sides and the height.

Using the Pythagorean theorem:
\[
m^2 = \text{(height)}^2 + (\text{difference in side lengths})^2
\]
Here:
\[
m^2 = 60^2 + (50 - 25)^2
\]
Let's calculate this:

\[
m^2 = 3600 + 25^2 = 3600 + 625 = 4225
\]
\[
m = \sqrt{4225} = 65
\]

Thus, the value of \( m \) is 65 units.

Would you like further clarification or details on this solution?

Here are five related questions to expand your understanding:

1. How would the solution change if the side lengths were different?
2. What other methods can be used to find the length of a diagonal in a trapezoid?
3. How is the Pythagorean theorem applied in other types of polygons?
4. What happens to the diagonal if the height of the trapezoid is doubled?
5. How does knowing the area of the trapezoid help in finding other dimensions?

**Tip:** The Pythagorean theorem is a powerful tool for solving problems involving right triangles and can be extended to more complex shapes by breaking them into simpler triangles.

Solve the trapezoid problem by finding the diagonal m using the Pythagorean theorem. With given sides of 25 and 50 units, and a height of 60 units, this problem explains the step-by-step method for applying the Pythagorean theorem to trapezoids. Suitable for students in Grades 8-10.

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