Triangle ABC is equilateral with altitude 6 sqrt(3). Find the perimeter of triangle ABC

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Triangle ABC is equilateral with altitude 6 sqrt(3). Find the perimeter of triangle ABC

[From: ] [author: ] [Date: 11-08-22] [Hit: ]

2 (hypotenuse), sqrt(3) (altitude).The altitude of your triangle is 6sqrt(3).Multiply the hypotenuse by 6 to get the length of one side.Your perimeter is 36.-Let s be a side of the equilateral triangle.......

please show all work!

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use Pythagorian's
side of the triangle =s
s²=(6√3)²+(s/2)²
solve for s
P=3s

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The altitude divides the equilateral triangle into two 30-60-90 triangles.

The sides of the 30-60-90 triangle are proportional to 1 (base), 2 (hypotenuse), sqrt(3) (altitude).

The altitude of your triangle is 6sqrt(3). Multiply the hypotenuse by 6 to get the length of one side.

Your perimeter is 36.

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Let s be a side of the equilateral triangle.

s√3/2 = 6√3

s = 12

Perimeter = (12)(3) = 36

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