To solve this problem, we need to understand the properties of midsegments in a triangle. The midsegment theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

In this figure:

1. $\triangle IJK$ is formed by connecting the midpoints of $\triangle FGH$.
2. Given that $JK = 6$ and $IJ = 7$, these segments are midsegments of $\triangle FGH$.
3. The midsegment $JK$ is parallel to side $FH$ and is half its length.

To find the length of $FH$: $FH = 2 \times JK = 2 \times 6 = 12$

Answer:

The length of $FH$ is $\mathbf{12}$.

Would you like further details on midsegment properties or have any questions?

Here are some related questions for further exploration:

1. How do we determine midpoints in a triangle with given coordinates?
2. Why does the midsegment theorem ensure parallelism and proportionality?
3. How can we find the area of smaller triangles within $\triangle FGH$ using given lengths?
4. What if the triangle is not drawn to scale; how does it affect our calculations?
5. How does this theorem apply in coordinate geometry?

Tip: Remember, midsegments are always half the length of the side they are parallel to in a triangle.