Question

What is the value of hin the figure below? In this diagram, ABAD ~ ACBD.

Answer 1

Answer:

  F.  8

Step-by-step explanation:

The ratio of the long side to the short side is the same in similar triangles. The long side of triangle BAD is AD, which has length 20-4 = 16.

  BD/DE = AD/BD

  h/4 = 16/h

  h^2 = 64 . . . . . . . multiply by 4h

  h = 8 . . . . . . . . . . take the square root (matches selection F)

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Comment on this geometry

BD = √(AD·DC) is called the "geometric mean" of the segments AD and DC. This geometry has some other geometric mean relationships as well:

BC = √(AC·DC)

BA = √(AC·AD)