https://file.aiquickdraw.com/mathbot/file/1727440131486869cv4vx.jpg

In the image, we are asked to find the length of segment \( FH \). The line segment \( FG \) is broken into two parts: \( FH \) and \( HG \). We are given the following information:

- The length of \( FG \) is 53 units.
- The length of \( HG \) is 40 units.

Using this information, we can set up the equation:
\[
FH + HG = FG
\]
Substitute the given values into the equation:
\[
FH + 40 = 53
\]

Now, solve for \( FH \):
\[
FH = 53 - 40 = 13
\]

Thus, the length of segment \( FH \) is 13 units.

Do you want more details or have any further questions? Here are some related questions to explore:

1. If \( FH \) was unknown but \( FG \) was smaller, how would that affect \( FH \)?
2. Can you explain why we used a linear equation to solve this?
3. What other geometric problems can be solved using the same reasoning?
4. How can this type of calculation be applied in real-life contexts?
5. What happens if the sum of \( FH \) and \( HG \) exceeds \( FG \)?

**Tip:** In problems with line segments, remember that the total length is always the sum of its parts. This can be generalized to various geometric figures as well!

Find FH in the line segment where FG = 53 units and HG = 40 units.

Learn how to find the length of a line segment FH when given FG = 53 units and HG = 40 units. This problem uses basic algebraic and geometric principles, including the Segment Addition Postulate, to determine that FH = 13 units. Ideal for students in Grades 6-8.

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