GRE Math : How to find the perimeter of an equilateral triangle
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Example Question #1 : Equilateral Triangles
Find the perimeter of an equilateral triangle with a height of 
None of the answer choices are correct.
Perimeter is found by adding up all sides of the triangle. All sides in an equilateral triangle are equal, so we need to find the value of just one side to know the values of all sides.
The height of an equilateral triangle divides it into two equal 30:60:90 triangles, which will have side ratios of 1:2:√3. The height here is the √3 ratio, which in this case is equivalent to 8, so to get the length of the other two sides, we put 8 over √3 (8/√3) and 2 * 8/√3 = 16/√3, which is the hypotenuse of our 30:60:90 triangle.
The perimeter is then 3 * 16/√3, or 48/√3.
Example Question #2 : How To Find The Perimeter Of An Equilateral Triangle
If the height of an equilateral triangle is 
By having a height in an equilateral triangle, the angle is bisected therefore creating two 
The height is opposite the angle 
Side opposite 
Since each side is the same and there are three sides, we just multply the answer by three to get 
Example Question #2 : How To Find The Perimeter Of An Equilateral Triangle
If area of equilateral triangle is 
The area of an equilateral triangle is 
So let's set-up an equation to solve for 
The 
Then take square root on both sides and we get 
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