GMAT Math : Calculating the length of the side of an equilateral triangle

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Example Question #1 : Equilateral Triangles

If an equilateral triangle has a perimeter of , what is the length of each side?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

An equilateral triangle has three equal sides; therefore, to find the length of each side, divide the perimeter by :

$\frac{18}{3}= 6$

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Example Question #1 : Equilateral Triangles

If the area of an equilateral is , given a height of , what is the base of the triangle?

Possible Answers:

4.8

Correct answer:

4.8

Explanation:

We derive the equation of base of a triangle from the area of a triangle formula:

$A=\frac{bh}{2}$

$b=\frac{2A}{h}$

$b=\frac{2*12}{5}$

b=4.8

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Example Question #3 : Calculating The Length Of The Side Of An Equilateral Triangle

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The height of an equilateral triangle ABC is . What is the length of side ?

Possible Answers:

$\frac{5}{\sqrt{3}}$

$2\sqrt{3}$

$\frac{10}{\sqrt{3}}$

$3\sqrt{5}$

Correct answer:

$\frac{10}{\sqrt{3}}$

Explanation:

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

$s=\frac{2h}{\sqrt{3}}$ , where is the length of the height.

Therefore, the final answer is

$\frac{2\cdot 5}{\sqrt3}=\frac{10}{\sqrt{3}}$ .

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Example Question #1 : Equilateral Triangles

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Equilateral triangle ABC is inscribed in a circle with radius , what is the length of a side of the triangle?

Possible Answers:

$\frac{15}{\sqrt{3}}$

$5\sqrt{3}$

$\frac{15}{2}$

$\sqrt{5}$

$3\sqrt{5}$

Correct answer:

$\frac{15}{\sqrt{3}}$

Explanation:

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 $\frac{2}{3}$ away from the edge of a given height.

Therefore 5, the radius of the circle is $\frac{2}{3}$ of the height.

Therefore, the height must be $\frac{15}{2}$ .

From here, we can use the formula for the height of the equilateral triangle $h=s\frac{\sqrt{3}}{2}$ , where is the length of the height and is the length of a side of the equilateral triangle.

Therefore, $s=2\frac{h}{\sqrt{3}}$ , then $\frac{15}{\sqrt{3}}$ is the final answer.

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GMAT Math : Calculating the length of the side of an equilateral triangle

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Equilateral Triangles

Example Question #1 : Equilateral Triangles

Example Question #3 : Calculating The Length Of The Side Of An Equilateral Triangle

Example Question #1 : Equilateral Triangles

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