Final answer:
The perpendicular distance from F to GH in an equilateral triangle with a side length of 2 cm is found using the formula for the height of an equilateral triangle, which results in approximately 1.732 cm.
Step-by-step explanation:
The student is seeking to find the perpendicular distance from vertex F to side GH in an equilateral triangle FGH with each side measuring 2 cm. The perpendicular distance from a vertex to the opposite side of an equilateral triangle is also the height or altitude of the triangle. To calculate the perpendicular distance (height), we can use the formula for the height of an equilateral triangle, which is height = (\sqrt{3}/2) × side. So, for the given triangle FGH with a side of 2 cm:
- Height = (\sqrt{3}/2) × 2 cm
- Height = \sqrt{3} cm ≈ 1.732 cm
Therefore, the perpendicular distance from F to GH is approximately 1.732 cm.