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This problem involves a triangle \( IJK \) formed by connecting the midpoints of the sides of a larger triangle \( FGH \). The key insight is that \( IJK \) is the medial triangle of \( FGH \), which means the sides of \( IJK \) are half the lengths of the sides of \( FGH \).

The lengths of the sides of triangle \( IJK \) are given as:
- \( IJ = 5 \)
- \( JK = 6 \)
- \( IK = 5 \)

Since \( IJK \) is the medial triangle, the sides of triangle \( FGH \) are double these lengths. Therefore, the lengths of the sides of triangle \( FGH \) are:
- \( FG = 2 \times 5 = 10 \)
- \( GH = 2 \times 6 = 12 \)
- \( FH = 2 \times 5 = 10 \)

Now, we can find the perimeter of triangle \( FGH \) by adding these side lengths:
\[
\text{Perimeter of } FGH = 10 + 12 + 10 = 32
\]

Thus, the perimeter of triangle \( FGH \) is \( 32 \) units.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the definition of a medial triangle?
2. How do the areas of triangle \( IJK \) and triangle \( FGH \) compare?
3. Can this method be applied to any triangle?
4. What is the relationship between the angles of triangles \( IJK \) and \( FGH \)?
5. How does the perimeter of \( IJK \) compare to the perimeter of \( FGH \)?

**Tip:** In any triangle, the medial triangle’s perimeter is half the perimeter of the original triangle.

Triangle IJK is formed by connecting the midpoints of the sides of triangle FGH. The lengths of the sides of triangle IJK are shown. Find the perimeter of triangle FGH.

Discover how to find the perimeter of a triangle by using the medial triangle theorem. This geometry problem involves triangles IJK and FGH, where triangle IJK connects the midpoints of FGH's sides. Learn how the side lengths relate and how to apply the perimeter formula for an insightful solution. Suitable for students in Grades 8-10.

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