Calculating the length of the side of an equilateral triangle - GMAT Quantitative
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If an equilateral triangle has a perimeter of
, what is the length of each side?
If an equilateral triangle has a perimeter of , what is the length of each side?
An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by
:

An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by :
Compare your answer with the correct one above
If the area of an equilateral is
, given a height of
, what is the base of the triangle?
If the area of an equilateral is , given a height of
, what is the base of the triangle?
We derive the equation of base of a triangle from the area of a triangle formula:




We derive the equation of base of a triangle from the area of a triangle formula:
Compare your answer with the correct one above

The height of an equilateral triangle
is
. What is the length of side
?
The height of an equilateral triangle is
. What is the length of side
?
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Compare your answer with the correct one above

Equilateral triangle
is inscribed in a circle with radius
, what is the length of a side of the triangle?
Equilateral triangle is inscribed in a circle with radius
, what is the length of a side of the triangle?
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located
away from the edge of a given height.
Therefore 5, the radius of the circle is
of the height.
Therefore, the height must be
.
From here, we can use the formula for the height of the equilateral triangle
, where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore,
, then
is the final answer.
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located away from the edge of a given height.
Therefore 5, the radius of the circle is of the height.
Therefore, the height must be .
From here, we can use the formula for the height of the equilateral triangle , where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore, , then
is the final answer.
Compare your answer with the correct one above
If an equilateral triangle has a perimeter of
, what is the length of each side?
If an equilateral triangle has a perimeter of , what is the length of each side?
An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by
:

An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by :
Compare your answer with the correct one above
If the area of an equilateral is
, given a height of
, what is the base of the triangle?
If the area of an equilateral is , given a height of
, what is the base of the triangle?
We derive the equation of base of a triangle from the area of a triangle formula:




We derive the equation of base of a triangle from the area of a triangle formula:
Compare your answer with the correct one above

The height of an equilateral triangle
is
. What is the length of side
?
The height of an equilateral triangle is
. What is the length of side
?
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Compare your answer with the correct one above

Equilateral triangle
is inscribed in a circle with radius
, what is the length of a side of the triangle?
Equilateral triangle is inscribed in a circle with radius
, what is the length of a side of the triangle?
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located
away from the edge of a given height.
Therefore 5, the radius of the circle is
of the height.
Therefore, the height must be
.
From here, we can use the formula for the height of the equilateral triangle
, where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore,
, then
is the final answer.
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located away from the edge of a given height.
Therefore 5, the radius of the circle is of the height.
Therefore, the height must be .
From here, we can use the formula for the height of the equilateral triangle , where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore, , then
is the final answer.
Compare your answer with the correct one above
If an equilateral triangle has a perimeter of
, what is the length of each side?
If an equilateral triangle has a perimeter of , what is the length of each side?
An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by
:

An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by :
Compare your answer with the correct one above
If the area of an equilateral is
, given a height of
, what is the base of the triangle?
If the area of an equilateral is , given a height of
, what is the base of the triangle?
We derive the equation of base of a triangle from the area of a triangle formula:




We derive the equation of base of a triangle from the area of a triangle formula:
Compare your answer with the correct one above

The height of an equilateral triangle
is
. What is the length of side
?
The height of an equilateral triangle is
. What is the length of side
?
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Compare your answer with the correct one above

Equilateral triangle
is inscribed in a circle with radius
, what is the length of a side of the triangle?
Equilateral triangle is inscribed in a circle with radius
, what is the length of a side of the triangle?
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located
away from the edge of a given height.
Therefore 5, the radius of the circle is
of the height.
Therefore, the height must be
.
From here, we can use the formula for the height of the equilateral triangle
, where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore,
, then
is the final answer.
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located away from the edge of a given height.
Therefore 5, the radius of the circle is of the height.
Therefore, the height must be .
From here, we can use the formula for the height of the equilateral triangle , where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore, , then
is the final answer.
Compare your answer with the correct one above
If an equilateral triangle has a perimeter of
, what is the length of each side?
If an equilateral triangle has a perimeter of , what is the length of each side?
An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by
:

An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by :
Compare your answer with the correct one above
If the area of an equilateral is
, given a height of
, what is the base of the triangle?
If the area of an equilateral is , given a height of
, what is the base of the triangle?
We derive the equation of base of a triangle from the area of a triangle formula:




We derive the equation of base of a triangle from the area of a triangle formula:
Compare your answer with the correct one above

The height of an equilateral triangle
is
. What is the length of side
?
The height of an equilateral triangle is
. What is the length of side
?
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Compare your answer with the correct one above

Equilateral triangle
is inscribed in a circle with radius
, what is the length of a side of the triangle?
Equilateral triangle is inscribed in a circle with radius
, what is the length of a side of the triangle?
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located
away from the edge of a given height.
Therefore 5, the radius of the circle is
of the height.
Therefore, the height must be
.
From here, we can use the formula for the height of the equilateral triangle
, where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore,
, then
is the final answer.
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located away from the edge of a given height.
Therefore 5, the radius of the circle is of the height.
Therefore, the height must be .
From here, we can use the formula for the height of the equilateral triangle , where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore, , then
is the final answer.
Compare your answer with the correct one above
If an equilateral triangle has a perimeter of
, what is the length of each side?
If an equilateral triangle has a perimeter of , what is the length of each side?
An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by
:

An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by :
Compare your answer with the correct one above
If the area of an equilateral is
, given a height of
, what is the base of the triangle?
If the area of an equilateral is , given a height of
, what is the base of the triangle?
We derive the equation of base of a triangle from the area of a triangle formula:




We derive the equation of base of a triangle from the area of a triangle formula:
Compare your answer with the correct one above

The height of an equilateral triangle
is
. What is the length of side
?
The height of an equilateral triangle is
. What is the length of side
?
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Similarily, we can use the same formula for the height to find the length of the side of an equilateral triangle, which is given by
, where
is the length of the height.
Therefore, the final answer is
.
Compare your answer with the correct one above

Equilateral triangle
is inscribed in a circle with radius
, what is the length of a side of the triangle?
Equilateral triangle is inscribed in a circle with radius
, what is the length of a side of the triangle?
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located
away from the edge of a given height.
Therefore 5, the radius of the circle is
of the height.
Therefore, the height must be
.
From here, we can use the formula for the height of the equilateral triangle
, where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore,
, then
is the final answer.
Since we are given the radius, we should be able to find the height of the equilateral triangle. Indeed, the center of the circle is at the intersections of the heights of the triangle, and is located away from the edge of a given height.
Therefore 5, the radius of the circle is of the height.
Therefore, the height must be .
From here, we can use the formula for the height of the equilateral triangle , where
is the length of the height and
is the length of a side of the equilateral triangle.
Therefore, , then
is the final answer.
Compare your answer with the correct one above