SOLUTION: How do I find the altitude of an equilateral triangle whose perimeter is 60 meters? I think you're supposed to divide the triangle by 3 because it has 3 sides and then multiply tha

Question 702431: How do I find the altitude of an equilateral triangle whose perimeter is 60 meters? I think you're supposed to divide the triangle by 3 because it has 3 sides and then multiply that answer by one half to get the altitude, is this correct?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
60/3 = 20

Each side is 20 meters.

Then you cut this side in half to get 10 meters. Draw a perpendicular line from one vertex to the midpoint of the opposite side. Call this length h (for height)

By the pythagorean theorem

h^2 + 10^2 = 20^2

h^2 + 100 = 400

h^2 = 400 - 100

h^2 = 300

h = sqrt(300)

h = sqrt(100*3)

h = sqrt(100)*sqrt(3)

h = 10*sqrt(3)

So the height or altitude is exactly 10*sqrt(3) meters long.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you divide the perimeter of an equilateral triangle by 3, you will get the measure of one side. If you construct an altitude in the triangle, you will make a 30-60-90 right triangle where one side of the equilateral triangle is the hypotenuse of the right triangle and the short leg is one-half of a side of the equilateral triangle. Since the sides of a 30-60-90 triangle are in proportion:

you need to multiply the measure of the side of the equilateral triangle times to get the altitude of the equilateral triangle.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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