In the diagram below, is an altitude of def. what is the length of ? if necessary, round your answer to two decimal places.

1st Method:

Right triangles EGD and FGE are similar:
(∠G =90, ∠F=∠EDG - having their sides respectively perpendicular)

Then we can write:

EG/FG = GD/GE
7/4 = GD/7 , by cross multiplication→ 7² = 4.GD→ 49 = 4.GD and GD=12.5

2nd Method:

The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse:

Then EG² = DG x GF
7² = 4 x GD and GD = 49/4 = 12.5