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The length of one side of an equilateral triangle is 6 square root 3 meters. Find the length of one altitude of the triangle.

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gmany

Answer:

9 m

Step-by-step explanation:

The formula of an altitude of an equilateral traingle with side a:

[tex]h=\dfrac{a\sqrt3}{2}[/tex]

We have [tex]a=6\sqrt3[/tex]

Substitute:

[tex]h=\dfrac{6\sqrt3\cdot\sqrt3}{2}=\dfrac{(6)(\sqrt3)^2}{2}[/tex]

Use [tex]\left(\sqrt{a}\right)^2=a[/tex]

[tex]h=\dfrac{(6)(3)}{2}=\dfrac{18}{2}=9[/tex]

The altitude of the equilateral triangle  with sides 6√3 meters is 9 meters.

Properties of equilateral triangle

  • All the sides are equal
  • All the angles are equal(60 degree each)

The length of the sides are 6√3 meters each. Recall triangles has three sides.

Therefore, the altitude or height of the triangle can be found as follows:

Using Pythagoras theorem,

c² = a² + b²

where

c = hypotenuse

a and b are the other 2 legs.

Therefore,

h² = (6√3)² - (1 /2 (6√3))²

h² = 108 - 27

h = √81

h = 9 meters

Therefore, the altitude of the triangle is 9 meters.

learn more on triangle here: https://brainly.com/question/8224697?referrer=searchResults

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