As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular  BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()
Choices:
A:\frac{24}{5}cm
B:4cm
C:\frac{24}{7}cm
D:5cm
Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
Question: As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular  BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()
Choices:
A:\frac{24}{5}cm
B:4cm
C:\frac{24}{7}cm
D:5cm
Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular  BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()
Choices:
A:\frac{24}{5}cm
B:4cm
C:\frac{24}{7}cm
D:5cm