GMAT Math : Geometry
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Example Questions
Example Question #1 : Calculating The Height Of An Equilateral Triangle
If the area of an equilateral is 
We derive the height formula from the area of the triangle formula:
Example Question #2 : Calculating The Height Of An Equilateral Triangle
What is the height of an equilateral triangle with sidelength 20?
The area of an equilateral triangle with sidelength 
Using this area for 
Example Question #551 : Problem Solving Questions
An equilateral triangle has a side length of 
The height of an upright equilateral triangle is the perpendicular distance from the center of its base to its top. We can imagine that this line cuts the equilateral triangle into two congruent right triangles whose height is half the length of the original base and whose hypotenuse is the original side length. In these two congruent triangles, their base, which is the height of the equilateral triangle, is the only unknown side length, so we can use the Pythagorean theorem to solve for it:
Example Question #1 : Calculating The Height Of An Equilateral Triangle
We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:
Therefore, the final answer is 
Example Question #1 : Calculating The Height Of An Equilateral Triangle
Given that an equilateral triangle has side lengths equal to 
To solve, we must use pythagorean's theorem given that we know the hypotenuse is 
Example Question #551 : Problem Solving Questions
The area of an equilateral triangle 
The area is given, which will allow us to calculate the side of the triangle and hence we can also find the perimeter.
The area for an equilateral triangle is given by the formula
Therefore, 
Thus 
Example Question #552 : Problem Solving Questions
A given equilateral triangle has a side length of 
Not enough information provided.
An equilateral triangle with a side length 
Given:
Example Question #3 : Calculating The Perimeter Of An Equilateral Triangle
A given equilateral triangle has a side length of 
An equilateral triangle with a side length 
Given:
Example Question #4 : Calculating The Perimeter Of An Equilateral Triangle
A given equilateral triangle has a side length of 
Not enough information provided.
An equilateral triangle with a side length 
Given:
Example Question #3 : Calculating The Perimeter Of An Equilateral Triangle
Given the following regarding Triangle 
I)
II) Side 
What is the length of side 
The trick to this one is to carefully put together what you are given.
We know that two of our angles are equal to 60 degrees. This means that the last angle is also 60 degrees. This make HFT an equilateral triangle.
Equilateral triangles always have equal sides and equal angles, so our last side has to be 7 light years as well.
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