Calculating the height of an equilateral triangle - GMAT Quantitative Reasoning
Card 0 of 5
If the area of an equilateral is 
, given a base of 
, what is the height of the triangle?
If the area of an equilateral is
We derive the height formula from the area of the triangle formula:
We derive the height formula from the area of the triangle formula:
Compare your answer with the correct one above
What is the height of an equilateral triangle with sidelength 20?
What is the height of an equilateral triangle with sidelength 20?
The area of an equilateral triangle with sidelength 
is
Using this area for 
and 20 for 
in the general triangle formula, we can obtain 
:
The area of an equilateral triangle with sidelength
Using this area for
Compare your answer with the correct one above
is an equilateral triangle, with a side length of 
. What is the height of the triangle?
We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:
, where 
is the length of a side and 
the length of the height.
Therefore, the final answer is 
.
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
Compare your answer with the correct one above
An equilateral triangle has a side length of 
. What is the height of the triangle?
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:
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:
Compare your answer with the correct one above
Given that an equilateral triangle has side lengths equal to 
, determine it's height in simplest form.
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 
and one side length is 
. Therefore:
To solve, we must use pythagorean's theorem given that we know the hypotenuse is
Compare your answer with the correct one above