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

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #84 : Plane Geometry

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 #85 : Plane Geometry

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.

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