GMAT Math : Triangles

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Next →

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

Report an Error

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

Report an Error

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

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

Possible Answers:

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

$10 \sqrt{3}$

$5 \sqrt{3}$

$10 \sqrt{2}$

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 :

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

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

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

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

$h=10\sqrt{3}$

Report an Error

Example Question #3 : Calculating The Height Of An Equilateral Triangle

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

Possible Answers:

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

$5\sqrt{2}$

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

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

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

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

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

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

Report an Error

Example Question #4 : Calculating The Height Of An Equilateral Triangle

Export-png__3_

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

Possible Answers:

$2\sqrt{3}$

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

$\frac{3}{2}$

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

$3\sqrt{3}$

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

Report an Error

Example Question #5 : 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:

$\sqrt6$

$3\sqrt3$

$\sqrt{27}$

$\sqrt{28}$

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:

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

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

Report an Error

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

Export-png__3_

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

Possible Answers:

$3\sqrt{3}$

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

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

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

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

Report an Error

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

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

Possible Answers:

45cm

Not enough information provided.

18cm

36cm

27cm

Correct answer:

27cm

Explanation:

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

Given:

x=9cm ,

P=3(9cm)=27cm .

Report an Error

Example Question #3 : Calculating The Perimeter Of An Equilateral Triangle

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

Possible Answers:

8.5cm

85cm

68cm

34cm

51cm

Correct answer:

51cm

Explanation:

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

Given:

x=17cm ,

P=3(17cm)=51cm .

Report an Error

Example Question #4 : 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:

63cm

42cm

10.5cm

84cm

Not enough information provided.

Correct answer:

63cm

Explanation:

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

Given:

x=21cm ,

P=3(21cm)=63cm .

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Next →

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Boston, Calculus Tutors in San Diego, ACT Tutors in Houston, GRE Tutors in Denver, Biology Tutors in Denver, LSAT Tutors in Phoenix, Statistics Tutors in San Francisco-Bay Area, Spanish Tutors in Boston, Statistics Tutors in Atlanta, MCAT Tutors in San Diego

Popular Courses & Classes

SSAT Courses & Classes in Denver, GRE Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC, ISEE Courses & Classes in Philadelphia, LSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Chicago, ACT Courses & Classes in Miami, Spanish Courses & Classes in Houston, ISEE Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia

Popular Test Prep

ACT Test Prep in Philadelphia, SAT Test Prep in San Diego, MCAT Test Prep in Seattle, ISEE Test Prep in Atlanta, ACT Test Prep in Denver, GRE Test Prep in Seattle, SAT Test Prep in Denver, GRE Test Prep in Denver, ACT Test Prep in Los Angeles, SSAT Test Prep in San Francisco-Bay Area

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

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 #3 : Calculating The Height Of An Equilateral Triangle

Example Question #4 : Calculating The Height Of An Equilateral Triangle

Example Question #5 : Calculating The Height Of An Equilateral Triangle

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

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

Example Question #3 : Calculating The Perimeter Of An Equilateral Triangle

Example Question #4 : Calculating The Perimeter Of An Equilateral Triangle

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details