GRE Math : How to find the length of the side of an equilateral triangle

Example Questions

Example Question #1 : Equilateral Triangles

What is the length of a side of an equilateral triangle if the area is ?

Possible Answers:

Correct answer:

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  as the final answer.

Example Question #1 : Equilateral Triangles

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

Possible Answers:

Correct answer:

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.