GMAT Math : Acute / Obtuse 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 #592 : Problem Solving Questions

What is the area, to the nearest whole square inch, of a triangle with sides 12, 13, and 15 inches?

Possible Answers:

None of the other answers are correct.

$\small 280 \; in^{2}$

$\small 98 \; in^{2}$

$\small 75 \; in^{2}$

$\small 78 \; in^{2}$

Correct answer:

$\small 75 \; in^{2}$

Explanation:

Use Heron's formula:

$\small A = \sqrt{s (s-a) (s-b)(s-c)}$

where $\small a = 12, b= 13, c = 15$ , and

$\small s = \frac{a + b + c}{2} = \frac{12 + 13 + 15}{2} = 20$

$\small A = \sqrt{s (s-a) (s-b)(s-c)}$

$\small \small \small A = \sqrt{20 (20-12) (20-13)(20-15)}$

$\small A = \sqrt{20 \cdot 8\cdot 7\cdot 5} = \sqrt{5,600} \approx 75$

Report an Error

Example Question #1 : Calculating The Area Of An Acute / Obtuse Triangle

Calculate the area of the triangle (not drawn to scale).

Possible Answers:

Correct answer:

Explanation:

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

In this problem, the base is 12 and the height is 6. Therefore:

$A=\frac{1}{2}(12)(6)=36$

Report an Error

Example Question #2 : Calculating The Area Of An Acute / Obtuse Triangle

Note: Figure NOT drawn to scale.

What is the area of the above figure?

Possible Answers:

256

352

224

More information is needed to answer this question.

240

Correct answer:

240

Explanation:

The figure is a composite of a rectangle and a triangle, as shown:

Split_arrow

The rectangle has area $A_ {1}= LW = 16 \cdot8 = 128$

The triangle has area $A_ {2} = \frac{1}{2} bh = \frac{1}{2} \cdot 14 \cdot 16 = 112$

The total area of the figure is $A_ {1} + A_ {2} = 128 + 112 = 240$

Report an Error

Example Question #592 : Gmat Quantitative Reasoning

Which of the following cannot be the measure of the vertex angle of an isosceles triangle?

Possible Answers:

$90^{\circ }$

$60^{\circ }$

Each of the other choices can be the measure of the vertex angle of an isosceles triangle.

$179.9^{\circ }$

$0.01^{\circ}$

Correct answer:

Each of the other choices can be the measure of the vertex angle of an isosceles triangle.

Explanation:

The only restriction on the measure of the vertex angle of an isosceles triangle is the restriction on any angle of a triangle - that it fall between $0^{\circ }$ and $180^{\circ }$ , noninclusive. If is any number in that range, each base angle, the two being congruent, will measure $\frac{180 -N }{2}$ , which will fall in the acceptable range.

Since all of these measures fall in that range, the correct response is that all are allowed.

Report an Error

Example Question #31 : Acute / Obtuse Triangles

What is the area of the triangle on the coordinate plane formed by the -axis and the lines of the equations y = 4x and y + 2x = 18 ?

Possible Answers:

162

108

Correct answer:

Explanation:

The easiest way to solve this is to graph the three lines and to observe the dimensions of the resulting triangle. It helps to know the coordinates of the three points of intersection, which we can do as follows:

The intersection of y = 4x and the -axis - that is, the line y = 0 can be found with some substitution:

y = 4x

0 = 4x

0 = x

The lines intersect at (0,0)

The intersection of y + 2x = 18 and the -axis can be found the same way:

y + 2x = 18

0+ 2x = 18

2x = 18

x=9

These lines intersect at (9,0)

The intersection of y = 4x and y + 2x = 18 can be found via the substitution method:

y + 2x = 18

4x + 2x = 18

6x = 18

x=3

$y = 4x= 4 \cdot 3 = 12$

The lines intersect at (3,12)

The triangle therefore has these three vertices. It is shown below.

Triangle

As can be seen, it is a triangle with base 9 and height 12, so its area is

$A = \frac{1}{2} \cdot 9 \cdot 12 = 54$

Report an Error

Example Question #3 : Calculating The Area Of An Acute / Obtuse Triangle

What is the area of a triangle on the coordinate plane with its vertices on the points $\left ( 0, 3\right ), (0, -5), (6,9)$ ?

Possible Answers:

Correct answer:

Explanation:

The vertical segment connecting ( 0, 3 ) and (0, -5) can be seen as the base of this triangle; this base has length 3 - (-5) = 8 . The height is the perpendicular (horizontal) distance from (6,9) to this segment, which is 6, the same as the -coordinate of this point. The area of the triangle is therefore

$A = \frac{1}{2} \cdot 6 \cdot 8 = 24$ .

Report an Error

Example Question #597 : Problem Solving Questions

Which of the following is the area of a triangle on the coordinate plane with its vertices on the points (-7,0), (5,0), (M,N) , where M,N >0 ?

Possible Answers:

12N

12M

12MN

Correct answer:

Explanation:

We can view the horizontal segment connecting (-7,0), (5,0) , and (5,0) as the base; its length wiill be 5 - (-7) = 12 . The height will be the perpendicular (vertical) distance to this segment from the opposite point (M,N) , which is , the -coordinate; therefore, the area of the triangle will be half the product of these two numbers, or

$A = \frac{1}{2} \cdot 12 \cdot N = 6N$ .

Report an Error

Example Question #32 : Acute / Obtuse Triangles

Give the area of a triangle on the coordinate plane with vertices (0,0), (2,6), (5,2) .

Possible Answers:

Correct answer:

Explanation:

This can be illustrated by showing this triangle inscribed inside a rectangle whose vertices are (0,0), (5,0),(0,6),(5.6) :

Triangle

The area of the white triangle $A _{W}$ is the one whose area we calculate. To do this, we need the area of the square:

$A_{\square } = 5 \cdot6 = 30$

The area of the red triangle:

$A_{1} = \frac{1}{2} \cdot 5 \cdot 2 = 5$

The area of the green triangle:

$A_{2} = \frac{1}{2} \cdot 6 \cdot 2 = 6$

And the area of the beige triangle:

$A_{3} = \frac{1}{2} \cdot 4 \cdot 3 = 6$

The area of the white triangle will be as follows:

$A _{W} = A_{\square } - \left (A_{1} + A_{2} + A_{3} \right )$

= 30 - (5+6+6)

= 30 - 17 = 13

Report an Error

Example Question #1 : Calculating The Length Of The Side Of An Acute / Obtuse Triangle

Two sides of a triangle measure 5 inches and 11 inches. Which of the following statements correctly expresses the range of possible lengths of the third side ?

Possible Answers:

C > 6

6 < C < 16

0 < C < 11

5 < C < 11

0 < C < 16

Correct answer:

6 < C < 16

Explanation:

By the Triangle Inequality, the sum of the lengths of two shortest sides must exceed that of the third.

Case 1: is the greatest of the three sidelengths.

Then C < 5 + 11 = 16

Case 2: is not the greatest of the three sidelengths - that is, 11 is.

Then 11 < C + 5 , or, equivalently, 6 < C .

Therefore, 6 < C < 16 .

Report an Error

Example Question #1 : Calculating The Length Of The Side Of An Acute / Obtuse Triangle

The sides of a triangle are 4, 8, and an integer . How many possible values does have?

Possible Answers:

Correct answer:

Explanation:

If two sides are 4 and 8, then the third side must be greater than 8-4 and less than 8+4 . This means can be 5, 6, 7, 8, 9, 10, or 11.

Report an Error

All GMAT Math Resources

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

Popular Subjects

French Tutors in New York City, Physics Tutors in Denver, Biology Tutors in San Francisco-Bay Area, Algebra Tutors in San Diego, Biology Tutors in Phoenix, Reading Tutors in Washington DC, SSAT Tutors in San Francisco-Bay Area, ISEE Tutors in Philadelphia, French Tutors in San Diego, Math Tutors in Los Angeles

Popular Courses & Classes

MCAT Courses & Classes in Miami, SSAT Courses & Classes in Miami, GMAT Courses & Classes in Washington DC, GRE Courses & Classes in Chicago, SSAT Courses & Classes in San Diego, SSAT Courses & Classes in Washington DC, ACT Courses & Classes in Houston, ISEE Courses & Classes in San Diego, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in Los Angeles, ISEE Test Prep in Philadelphia, GRE Test Prep in Denver, LSAT Test Prep in Washington DC, ISEE Test Prep in Chicago, GRE Test Prep in San Diego, LSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Philadelphia, GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Houston

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 : Acute / Obtuse Triangles

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #592 : Problem Solving Questions

Example Question #1 : Calculating The Area Of An Acute / Obtuse Triangle

Example Question #2 : Calculating The Area Of An Acute / Obtuse Triangle

Example Question #592 : Gmat Quantitative Reasoning

Example Question #31 : Acute / Obtuse Triangles

Example Question #3 : Calculating The Area Of An Acute / Obtuse Triangle

Example Question #597 : Problem Solving Questions

Example Question #32 : Acute / Obtuse Triangles

Example Question #1 : Calculating The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #1 : Calculating The Length Of The Side Of An Acute / Obtuse Triangle

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details