GRE Math help » Geometry » plane Geometry » triangle » Equilateral triangle » just how to uncover the perimeter the an it is intended triangle

Find the perimeter that an it is provided triangle through a elevation of

*
.

You are watching: What is the perimeter of an equilateral triangle whose height is 2√3


*


*


*


*


Explanation:

Perimeter is discovered by adding up every sides that the triangle. All sides in an equilateral triangle room equal, so we need to uncover the worth of simply one side to know the worths of all sides. 

The height of an it is intended triangle divides it right into two equal 30:60:90 triangles, i beg your pardon will have actually side ratios that 1:2:√3. The elevation here is the √3 ratio, which in this case is equivalent to 8, for this reason to gain the length of the other two sides, we placed 8 over √3 (8/√3) and 2 * 8/√3 = 16/√3, i m sorry is the hypotenuse of our 30:60:90 triangle.

The perimeter is climate 3 * 16/√3, or 48/√3.


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Example concern #2 : how To discover The Perimeter the An equilateral Triangle


If the height of an it is provided triangle is 

*
, what is the perimeter?


Possible Answers:
Correct answer:

*


Explanation:

By having a height in an it is intended triangle, the edge is bisected therefore creating two 

*
 triangles.

The height is the contrary the angle 

*
. We have the right to set-up a proportion.

Side opposite 

*
 is 
*
 and the next of it is intended triangle i m sorry is opposite 
*
 is 
*
.

*
 Cross multiply.

*
 Divide both political parties by 
*

*
 Multiply top and also bottom by 
*
 to remove the radical.

*
 

Since every side is the same and also there space three sides, we just multply the prize by three to get 

*


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Example concern #3 : just how To uncover The Perimeter that An equilateral Triangle


If area of it is provided triangle is 

*
, what is the perimeter?


Possible Answers:
Correct answer:

*


Explanation:

The area the an equilateral triangle is 

*
.

So let"s set-up one equation to deal with for 

*

*
 Cross multiply.

*
 

The 

*
 cancels out and also we get 
*
.

Then take it square root on both sides and also we get 

*
. Since we have three equal sides, we simply multply 
*
 by 3 to get 
*
 as the last answer.

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