sksksksksjdn sksksksksjdn
  • 25-06-2018
  • Mathematics
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What is the length of the altitude of the equilateral triangle below?

What is the length of the altitude of the equilateral triangle below class=

Respuesta :

rejkjavik rejkjavik
  • 30-10-2018

we are given

equilateral triangle

we can see that triangle ACD is a right angled triangle

so, we can use Pythagoras theorem for this triangle

hypotenuse=AC

Adjacent=CD

opposite=AD=a

and

[tex]AC=6\sqrt{3}[/tex]

[tex]CD=3\sqrt{3}[/tex]

[tex]AD=a[/tex]

now, we can use Pythagoras theorem

and we get

[tex]AC^2=CD^2+AD^2[/tex]

now, we can plug values

[tex](6\sqrt{3} )^2=(3\sqrt{3} )^2+a^2[/tex]

now, we can solve for a

[tex]108=27+a^2[/tex]

[tex]27+a^2-27=108-27[/tex]

[tex]a^2=81[/tex]

[tex]a=9[/tex]

so, option-A..........Answer

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