GMAT Math : Triangles

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Example Questions

Example Question #1 : Calculating The Area Of An Equilateral Triangle

A given right triangle has a base of length and a height . What is the area of the triangle?

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

For a given right triangle with a side length and a height , the area is

$A=\frac{1}{2}bh$ . Plugging in the values provided:

$A=\frac{1}{2}(9)(8)$

$A=\frac{1}{2}(72)$

A=36

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Example Question #1 : Calculating The Height Of An Equilateral Triangle

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

Possible Answers:

Correct answer:

Explanation:

We derive the height formula from the area of the triangle formula:

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

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

$=\frac{(2*21)}{3}$

=14

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Example Question #2 : Calculating The Height Of An Equilateral Triangle

What is the height of an equilateral triangle with sidelength 20?

Possible Answers:

$10 \sqrt{2}$

$5 \sqrt{3}$

$\frac{10 \sqrt{2}}{3}$

$10 \sqrt{3}$

Correct answer:

$10 \sqrt{3}$

Explanation:

The area of an equilateral triangle with sidelength s = 20 is

$A = \frac{s^{2}\sqrt{3}}{4} = \frac{20^{2}\sqrt{3}}{4} = \frac{400\sqrt{3}}{4} = 100\sqrt{3}$

Using this area for and 20 for in the general triangle formula, we can obtain :

$\frac{1}{2} bh = A$

$\frac{1}{2}\cdot 20 \cdot h =100\sqrt{3}$

$10 \cdot h =100\sqrt{3}$

$10 \cdot h \div 10 =100\sqrt{3}\div 10$

$h=10\sqrt{3}$

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Example Question #551 : Problem Solving Questions

An equilateral triangle has a side length of . What is the height of the triangle?

Possible Answers:

$\frac{2\sqrt{5}}{3}$

$\frac{5\sqrt{3}}{2}$

$5\sqrt{2}$

$\frac{3\sqrt{2}}{5}$

Correct answer:

$\frac{5\sqrt{3}}{2}$

Explanation:

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:

a^2+b^2=c^2

$(\frac{5}{2})^2+b^2=5^2$

$b^2=5^2-(\frac{5}{2})^2=\frac{75}{4}$

$b=\sqrt{\frac{75}{4}}=\frac{\sqrt{3*25}}{2}=\frac{5\sqrt{3}}{2}$

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Example Question #61 : Triangles

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ABC is an equilateral triangle, with a side length of . What is the height of the triangle?

Possible Answers:

$3\sqrt{3}$

$2\sqrt{3}$

$\frac{\sqrt{3}}{2}$

$\frac{3}{2}$

$\frac{3\sqrt{3}}{2}$

Correct answer:

$\frac{3\sqrt{3}}{2}$

Explanation:

We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:

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

Therefore, the final answer is $\frac{3\sqrt{3}}{2}$ .

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Example Question #1 : Calculating The Height Of An Equilateral Triangle

Given that an equilateral triangle has side lengths equal to , determine it's height in simplest form.

Possible Answers:

$\sqrt{28}$

$\sqrt6$

$\sqrt{27}$

$3\sqrt3$

Correct answer:

$3\sqrt3$

Explanation:

To solve, we must use pythagorean's theorem given that we know the hypotenuse is and one side length is $\left (\frac{1}{2} \textup{ of } 6 \right )$ . Therefore:

$c^2=a^2+b^2\Rightarrow 6^2=a^2+3^2\Rightarrow 27=a^2$

$a=\sqrt{27}=\sqrt{3^2*3}=3\sqrt3$

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Example Question #61 : Triangles

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The area of an equilateral triangle ABC is . What is the perimeter of ABC ?

Possible Answers:

$3\sqrt{3}$

$3\sqrt{\frac{28}{\sqrt{3}}}$

$\frac{28}{\sqrt{3}}$

$3\sqrt{\frac{16}{\sqrt{3}}}$

Correct answer:

$3\sqrt{\frac{28}{\sqrt{3}}}$

Explanation:

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

$\frac{s^{2}\sqrt{3}}{4}$ , where is the length of the side of the triangle.

Therefore, $s=\sqrt{\frac{4a}{\sqrt{3}}}$ , where is the area.

Thus $s=\sqrt{\frac{28}{\sqrt{3}}}$ , and the perimeter of an equilateral triangle is three times the side, hence, the final answer is $3\sqrt{\frac{28}{\sqrt{3}}}$ .

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Example Question #62 : Triangles

A given equilateral triangle has a side length of 9cm . What is the perimeter of the triangle?

Possible Answers:

36cm

18cm

Not enough information provided.

45cm

27cm

Correct answer:

27cm

Explanation:

An equilateral triangle with a side length has a perimeter P=3x .

Given:

x=9cm ,

P=3(9cm)=27cm .

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Example Question #312 : Geometry

A given equilateral triangle has a side length of 17cm . What is the perimeter of the triangle?

Possible Answers:

8.5cm

34cm

68cm

85cm

51cm

Correct answer:

51cm

Explanation:

An equilateral triangle with a side length has a perimeter P=3x .

Given:

x=17cm ,

P=3(17cm)=51cm .

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Example Question #2 : Calculating The Perimeter Of An Equilateral Triangle

A given equilateral triangle has a side length of 21cm . What is the perimeter of the triangle?

Possible Answers:

84cm

42cm

Not enough information provided.

10.5cm

63cm

Correct answer:

63cm

Explanation:

An equilateral triangle with a side length has a perimeter P=3x .

Given:

x=21cm ,

P=3(21cm)=63cm .

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GMAT Math : Triangles

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Area Of An Equilateral Triangle

Example Question #1 : Calculating The Height Of An Equilateral Triangle

Example Question #2 : Calculating The Height Of An Equilateral Triangle

Example Question #551 : Problem Solving Questions

Example Question #61 : Triangles

Example Question #1 : Calculating The Height Of An Equilateral Triangle

Example Question #61 : Triangles

Example Question #62 : Triangles

Example Question #312 : Geometry

Example Question #2 : Calculating The Perimeter Of An Equilateral Triangle

All GMAT Math Resources

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