# GRE Math : How to find the perimeter of an equilateral triangle

## Example Questions

### Example Question #1 : How To Find The Perimeter Of An Equilateral Triangle

Find the perimeter of an equilateral triangle with a height of .

None of the answer choices are correct.

Explanation:

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 : Equilateral Triangles

If the height of an equilateral triangle is , what is the perimeter?

Explanation:

By having a height in an equilateral triangle, the angle is bisected therefore creating two  triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite  is  and the side of equilateral triangle which is opposite  is .

Cross multiply.

Divide both sides by

Multiply top and bottom by  to get rid of the radical.

Since each side is the same and there are three sides, we just multply the answer by three to get

### Example Question #1 : Equilateral Triangles

If area of equilateral triangle is , what is the perimeter?

Explanation:

The area of an equilateral triangle is .

So let's set-up an equation to solve for

Cross multiply.

The  cancels out and we get .

Then take square root on both sides and we get . Since we have three equal sides, we just multply  by three to get  as the final answer.

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