All GRE Math Resources
Example Question #4 : Equilateral Triangles
What is the length of a side of an equilateral triangle if the area is ?
The area of an equilateral triangle is .
So let's set-up an equation to solve for .
The cancels out and we get .
Then take square root on both sides and we get as the final answer.
Example Question #5 : Equilateral Triangles
If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?
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 .
Divide both sides by
Multiply top and bottom by to get rid of the radical.