heintzelmanvp6ir6d heintzelmanvp6ir6d
  • 25-01-2019
  • Mathematics
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Find the length of the altitude drawn to the hypotenuse. The triangle is not to scale.

Find the length of the altitude drawn to the hypotenuse The triangle is not to scale class=

Respuesta :

SociometricStar
SociometricStar SociometricStar
  • 04-02-2019

Answer:

D is the correct option.

Step-by-step explanation:

Let us apply the Pythagorean theorem in the right angle triangles.

In right angle triangle ABC

[tex]24^2=AB^2+AC^2......(1)[/tex]

Now, in right angle triangle ABD,

[tex]AB^2=AD^2+4^2\\AB^2=AD^2+16.......(2)[/tex]

Now, in right angle triangle ADC,

[tex]AC^2=AD^2+20^2\\\\AC^2=AD^2+400[/tex]

From equation (1) and (2)

[tex]24^2-AB^2=AD^2+400\\\\24^2-(AD^2+16)=AD^2+400\\\\576-AD^2-16=AD^2+400\\\\2AD^2=160\\\\AD^2=80\\\\AD=4\sqrt{5}[/tex]



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