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Given right triangle A, B, CABC with altitude start overline, B, D, end overline
BD
drawn to hypotenuse start overline, A, C, end overline
AC
. If A, D, equals, 20AD=20 and D, C, equals, 30, commaDC=30, what is the length of start overline, B, D, end overline
BD
in simplest radical form?

Picture down below

Given Right Triangle A B CABC With Altitude Start Overline B D End Overline BD Drawn To Hypotenuse Start Overline A C End Overline AC If A D Equals 20AD20 And D class=

Sagot :

sqdancefan

Answer:

  10√6

Step-by-step explanation:

You want the altitude BD in right triangle ABC, where it divides hypotenuse AC into the parts AD=20 and DC=30.

Geometric mean

The right triangles in the figure are all similar, so we have ...

  [tex]\dfrac{BD}{AD}=\dfrac{DC}{BD}\\\\BD=\sqrt{AD\cdot DC}=\sqrt{20\cdot30}\\\\\boxed{BD=10\sqrt{6}}[/tex]

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