moideenmkv
moideenmkv moideenmkv
  • 21-12-2019
  • Mathematics
contestada

In an equilateral triangle ABC of side 2a,AD perpendicular to BC,then find the length of AD.

Respuesta :

sam4040
sam4040 sam4040
  • 28-12-2019

Answer:

[tex]AD=\sqrt{3} \ a[/tex]

Step-by-step explanation:

AD is perpendicular on BC.

BD=CD=a (as D is the mid point of BC)

Now in the triangle ABD

[tex]AB^{2} =BD^{2} +AD^{2} \ \ \ \ (using \ Pythagorean \ Theorem)\\AD^2=AB^2-BD^2\\AD^2=(2a)^{2} -a^2\\AD^2=3a^2\\AD=a\sqrt{3}[/tex]

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