GMAT Math : Right 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

Example Question #1 : Right Triangles

Which set of side lengths cannot be the side lengths of a right triangle?

Possible Answers:

$\dpi{100} \small 45, 55,75$

$\dpi{100} \small 48,64,80$

$\dpi{100} \small 28,45,53$

$\dpi{100} \small 84,35,91$

$\dpi{100} \small 3,4,5$

Correct answer:

$\dpi{100} \small 45, 55,75$

Explanation:

For a triangle to be a right triangle, the sides must obey the Pythagorean Theorem. Let's try our options.

3, 4, 5: You should know this is a right triangle without having to do any calculations because it is one of the special triangles that you should remember. But if you didn't, $3^{2} + 4^{2} = 25 = 5^{2}$ .

28, 45, 53: $28^{2} + 45^{2} = 784 + 2025 = 2809 = 53^{2}$

45, 55, 75: $45^{2} + 55^{2} = 2025 + 3025 = 5050 \neq 75^{2}$ . The sides don't follow the Pythagorean Theorem so this can't be a right triangle. This is our answer. Let's check the remaining two sets of sides as well.

48, 64, 80: $48^{2} + 64^{2} = 2304 + 4096 = 6400 = 80^{2}$ . These are pretty big numbers and this math might take a while. Instead of doing these calculations, we could also see if 48, 64, and 80 look like any of the special triangles we know. Let's divide the three numbers by 16. 48/16 = 3, 64/16 = 4, and 80/16 = 5. Then this is just a type of 3,4,5 triangle, which we know is a right triangle.

84, 35, 91: $84^{2} + 35^{2} = 7056 + 1225 = 8281 = 91^{2}$ . Again, these are big numbers to square. Let's divide the three numbers by their greatest common factor, 7. 84/7 = 12, 35/7 = 5, 91/7 = 13. Then this is a 5, 12, 13 triangle, which is another of our special triangles that we know is a right triangle.

Report an Error

Example Question #2 : Triangles

Which of the following right triangles is similar to one with a height of and a base of ?

Possible Answers:

h=12,b=20

h=7,b=12

h=10,b=15

h=5,b=10

h=8,b=14

Correct answer:

h=10,b=15

Explanation:

In order for two right triangles to be similar, the ratio of their dimensions must be equal. First we can check the ratio of the height to the base for the given triangle, and then we can check each answer choice for the triangle with the same ratio:

$Given:\frac{h}{b}=\frac{6}{9}=\frac{2}{3}$

So now we can check the ratio of the height to the base for each answer option, in no particular order, and the one with the same ratio as the given triangle will be a triangle that is similar:

$Option1:\frac{h}{b}=\frac{5}{10}=\frac{1}{2}$

$Option2:\frac{h}{b}=\frac{7}{12}$

$Option3:\frac{h}{b}=\frac{8}{14}=\frac{4}{7}$

$Option4:\frac{h}{b}=\frac{12}{20}=\frac{3}{5}$

$Option5:\frac{h}{b}=\frac{10}{15}=\frac{2}{3}$

The triangle with a height of and a base of has the same ratio as the given triangle, so this one is similar.

Report an Error

Example Question #3 : Triangles

Which of the following right triangles is similar to one with a height of and a base of ?

Possible Answers:

h=3, b=5

h=6, b=2

h=2, b=6

h=3, b=1

h=7, b=14

Correct answer:

h=2, b=6

Explanation:

In order for two right triangles to be similar, their height-to-base ratios must be equal. Given a right triangle with a height h=4 and a base b=12 , the ratio $\frac{h}{b}=\frac{4}{12}=\frac{1}{3}$ . The only answer provided with a ratio of $\frac{1}{3}$ is h=2, b=6 .

Report an Error

Example Question #4 : Triangles

Which of the following right triangles is similar to one with a height of and a base of ?

Possible Answers:

h=3, b=12

h=6, b=18

h=10, b=4

h=2, b=12

h=7, b=35

Correct answer:

h=3, b=12

Explanation:

In order for two right triangles to be similar, their height-to-base ratios must be equal. Given a right triangle with a height h=5 and a base b=20 , the ratio $\frac{h}{b}=\frac{5}{20}=\frac{1}{4}$ . The only answer provided with a ratio of $\frac{1}{4}$ is h=3, b=12 .

Report an Error

Example Question #4 : Triangles

Which of the following right triangles is similar to one with a height of and a base of ?

Possible Answers:

h=5, b=30

None of the above

h=1, b=4

h=6, b=48

h=9, b=81 h=3, b=45

Correct answer:

h=5, b=30

Explanation:

In order for two right triangles to be similar, their height-to-base ratios must be equal. Given a right triangle with a height of and a base of , the ratio $\frac{h}{b}=\frac{7}{42}=\frac{1}{6}$ . The only answer provided with a ratio of $\frac{1}{6}$ is h=5, b=30 .

Report an Error

Example Question #6 : Right Triangles

Given two right triangles $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , with right angles $\angle B, \angle E$ , what is the measure of $\angle A$ ?

Statement 1: $\bigtriangleup ABC \sim \bigtriangleup DEF$

Statement 2: $\bigtriangleup ABC \sim \bigtriangleup FED$

Possible Answers:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

Explanation:

Corresponding angles of similar triangles are congruent, so Statement 1 alone establishes that $\angle A \cong \angle D$ and $\angle C \cong \angle F$ ; similarly, Statement 2 alone establishes that $\angle A \cong \angle F$ and $\angle C \cong \angle D$ . However, neither statement alone establishes the actual measure of any of the four acute angles.

Assume both statements are true. From transitivity, it holds that $\angle A \cong \angle D \cong \angle C$ . Specifically, the two acute angles of $\bigtriangleup ABC$ , one of which is $\angle A$ , are congruent. Since $\angle B$ is right, this makes $\bigtriangleup ABC$ and isosceles right triangle, and its acute angles, including $\angle A$ , have measure $45 ^{\circ }$ .

Report an Error

Example Question #1 : Right Triangles

What is the side length of a right triangle with a hypotenuse of and a side of ?

Possible Answers:

Correct answer:

Explanation:

We need to use the Pythagorean theorem:

a^2+b^2=c^2

a^2=c^2-b^2

a^2=10^2-8^2

a^2=100-64

a^2=36

a=6

Report an Error

Example Question #1 : Calculating The Length Of The Side Of A Right Triangle

There is a big square that consists of four identical right triangles and a small square. If the area of the small square is 1, the area of the big square is 5, what is the length of the shortest side of the right triangles?

Possible Answers:

$\dpi{100} \small 2$

$\dpi{100} \small 3$

$\dpi{100} \small 4$

$\dpi{100} \small 1$

$\dpi{100} \small 5$

Correct answer:

$\dpi{100} \small 1$

Explanation:

The area of the big square is 5, and area of the small square is 1. Therefore, the area of the four right triangles is $\dpi{100} \small 5-1=4$ .

Since the four triangles are all exactly the same, the area of each of the right triangle is 1. We know that the longer side is 2 times the shorter side, so we can represent the shorter side as $\dpi{100} \small x$ and the longer side as $\dpi{100} \small 2x$ . Then we are able to set up an equation:

$\dpi{100} \small \frac{1}{2}\times x\times 2x=1$ .

Therefore, x, the length of the shortest side of the right triangle, is 1.

Report an Error

Example Question #2 : Calculating The Length Of The Side Of A Right Triangle

A triangle has sides of length 9, 12, and 16. Which of the following statements is true?

Possible Answers:

The triangle is acute and isosceles.

The triangle is obtuse and scalene.

The triangle is acute and scalene.

The triangle cannot exist.

The triangle is obtuse and isosceles.

Correct answer:

The triangle is obtuse and scalene.

Explanation:

This triangle can exist by the Triangle Inequality, since the sum of the lengths of its shortest two sides exceeds that of the longest side:

9 + 12 = 21 > 16

The sum of the squares of its shortest two sides is less than the square of that of its longest side:

$9^{2}+12^{2} = 81+144= 225 <256=16^{2}$

This makes the triangle obtuse.

Its sides are all of different measure, which makes the triangle scalene as well.

Obtuse and scalene is the correct choice.

Report an Error

Example Question #7 : Right Triangles

Using the following right traingle, calculate the value of

(Not drawn to scale.)

Possible Answers:

$1\textup{ cm}$

$9\textup{ cm}$

$3\textup{ cm}$

$6.4\textup{ cm}$

Correct answer:

$3\textup{ cm}$

Explanation:

We can determine the length of the side by using the Pythagorean Theorem:

c^2=a^2+b^2

where c=5, a=4

Our equation is then:

5^2=x^2+4^2

x^2=25-16=9

x=3

Report an Error

All GMAT Math Resources

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

Popular Subjects

Math Tutors in Seattle, SSAT Tutors in Houston, Math Tutors in Atlanta, Chemistry Tutors in Phoenix, Statistics Tutors in Seattle, ISEE Tutors in Houston, GMAT Tutors in Chicago, LSAT Tutors in Denver, ISEE Tutors in Denver, Computer Science Tutors in Seattle

Popular Courses & Classes

SSAT Courses & Classes in Houston, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Philadelphia, ACT Courses & Classes in Los Angeles, LSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Atlanta, Spanish Courses & Classes in Houston, GRE Courses & Classes in Boston, LSAT Courses & Classes in Chicago, LSAT Courses & Classes in Seattle

Popular Test Prep

LSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Denver, GRE Test Prep in Boston, ACT Test Prep in Los Angeles, ISEE Test Prep in Phoenix, SSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Miami, SSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Seattle, MCAT Test Prep in Philadelphia

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 : Right Triangles

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Right Triangles

Example Question #2 : Triangles

Example Question #3 : Triangles

Example Question #4 : Triangles

Example Question #4 : Triangles

Example Question #6 : Right Triangles

Example Question #1 : Right Triangles

Example Question #1 : Calculating The Length Of The Side Of A Right Triangle

Example Question #2 : Calculating The Length Of The Side Of A Right Triangle

Example Question #7 : Right Triangles

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details