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In the diagram below, is an altitude of DEF. What is the length of ? If necessary, round your answer to two decimal places.

In the diagram below, is an altitude of DEF. What is the length of ? If necessary-example-1

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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
User Alex MDC
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