Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #71 : Triangles

In terms of , find the perimeter.

Possible Answers:

$6x+2x\sqrt3$

$4x+2x\sqrt3$

$8x+2x\sqrt3$

$2x+2x\sqrt3$

Correct answer:

$4x+2x\sqrt3$

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is and the hypotenuse is .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $2x, 2x, \text{ and }2x\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=2x+2x+2x\sqrt3=4x+2x\sqrt3$

Report an Error

Example Question #14 : How To Find The Perimeter Of An Acute / Obtuse Triangle

In terms of , find the perimeter.

Possible Answers:

$62x+42x\sqrt3$

$84x+42x\sqrt3$

$42x+42x\sqrt3$

$84+42x\sqrt3$

Correct answer:

$84x+42x\sqrt3$

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is 21x and the hypotenuse is 42x .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $42x, 42x, \text{ and }42x\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=42x+42x+42x\sqrt3=84x+42x\sqrt3$

Report an Error

Example Question #72 : Triangles

Find the perimeter of the triangle below. Round to the nearest tenths place.

Possible Answers:

59.7

59.1

58.3

47.8

Correct answer:

59.7

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is and the hypotenuse is .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $16, 16, \text{ and }16\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=16+16+16\sqrt3=59.7$

Report an Error

Example Question #73 : Triangles

In terms of , find the perimeter of the triangle.

Possible Answers:

$108x+36x\sqrt3$

$72x+36x\sqrt3$

$36x+36x\sqrt3$

$72+36x\sqrt3$

Correct answer:

$72x+36x\sqrt3$

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is 18x and the hypotenuse is 36x .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $36x, 36x, \text{ and }36x\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=36x+36x+36x\sqrt3=72x+36x\sqrt3$

Report an Error

Example Question #512 : Intermediate Geometry

A triangle is defined by the following points on a coordinate plane: (1, 5), (2, 12), (-3, 4)

What is the perimeter of the triangle?

Possible Answers:

21.67

25.06

22.49

20.63

Correct answer:

20.63

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(1, 5)\text{ and }(2, 12)$ as its endpoints.

$\text{side 1}=\sqrt{(2-1)^2+(12-5)^2}=\sqrt{50}=5\sqrt2$

The second side of the triangle is the line segment that has $(2, 12)\text{ and }(-3, 4)$ as its endpoints.

$\text{side 2}=\sqrt{(2-(-3))^2+(12-4)^2}=\sqrt{89}$

The third side of the triangle is the line segment that has $(-3, 4)\text{ and }(1, 5)$ as its endpoints.

$\text{side 3}=\sqrt{(1-(-3))^2+(5-4)^2}=\sqrt{17}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=5\sqrt{2} +\sqrt{89}+\sqrt{17}=20.63$

Make sure to round to places after the decimal.

Report an Error

Example Question #513 : Intermediate Geometry

A triangle is defined by the following points in a coordinate plane: (5, 6), (7, 2), (9, 11) .

What is the perimeter of the triangle?

Possible Answers:

26.78

20.09

22.13

24.59

Correct answer:

20.09

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(5, 6)\text{ and }(7, 2)$ as its endpoints.

$\text{side 1}=\sqrt{(7-5)^2+(2-6)^2}=\sqrt{20}=2\sqrt5$

The second side of the triangle is the line segment that has $(7, 2)\text{ and }(9, 11)$ as its endpoints.

$\text{side 2}=\sqrt{(9-7)^2+(11-2)^2}=\sqrt{85}$

The third side of the triangle is the line segment that has $(5, 6)\text{ and }(9, 11)$ as its endpoints.

$\text{side 3}=\sqrt{(9-5)^2+(11-6)^2}=\sqrt{41}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=2\sqrt{5} +\sqrt{85}+\sqrt{41}=20.09$

Make sure to round to places after the decimal.

Report an Error

Example Question #514 : Intermediate Geometry

A triangle is defined by the following points on a coordinate plane: (-5, 1), (6, -2), (7, 0) .

What is the perimeter of the triangle?

Possible Answers:

27.09

28.81

25.68

30.01

Correct answer:

25.68

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(-5, 1)\text{ and }(6, -2)$ as its endpoints.

$\text{side 1}=\sqrt{(6-(-5))^2+(-2-1)^2}=\sqrt{130}$

The second side of the triangle is the line segment that has $(6, -2)\text{ and }(7, 0)$ as its endpoints.

$\text{side 2}=\sqrt{(7-6)^2+(0-(-2))^2}=\sqrt{5}$

The third side of the triangle is the line segment that has $(-5, 1)\text{ and }(7, 0)$ as its endpoints.

$\text{side 3}=\sqrt{(7-(-5))^2+(0-1)^2}=\sqrt{145}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{130} +\sqrt{5}+\sqrt{145}=25.68$

Make sure to round to places after the decimal.

Report an Error

Example Question #515 : Intermediate Geometry

A triangle is defined by the following points on a coordinate plane: (9, 8), (12, 0), (-1, -2) .

What is the perimeter of the triangle?

Possible Answers:

36.09

35.84

33.87

31.45

Correct answer:

35.84

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(9, 8)\text{ and }(12, 0)$ as its endpoints.

$\text{side 1}=\sqrt{(12-9)^2+(0-8)^2}=\sqrt{73}$

The second side of the triangle is the line segment that has $(12, 0)\text{ and }(-1, -2)$ as its endpoints.

$\text{side 2}=\sqrt{(-1-12)^2+(-2-0)^2}=\sqrt{173}$

The third side of the triangle is the line segment that has $(9, 8)\text{ and }(-1, -2)$ as its endpoints.

$\text{side 3}=\sqrt{(-1-9))^2+(-2-8)^2}=\sqrt{200}=10\sqrt2$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{73} +\sqrt{173}+10\sqrt{2}=35.84$

Make sure to round to places after the decimal.

Report an Error

Example Question #77 : Triangles

A triangle is defined by the following points on a coordinate plane: (1, 1), (0, 5), (-9, -1) .

What is the perimeter of the triangle?

Possible Answers:

24.59

21.66

23.08

25.14

Correct answer:

25.14

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(1, 1)\text{ and }(0, 5)$ as its endpoints.

$\text{side 1}=\sqrt{(0-1)^2+(5-1)^2}=\sqrt{17}$

The second side of the triangle is the line segment that has $(0, 5)\text{ and }(-9, -1)$ as its endpoints.

$\text{side 2}=\sqrt{(-9-0)^2+(-1-5)^2}=\sqrt{117}$

The third side of the triangle is the line segment that has $(1, 1)\text{ and }(-9,-1)$ as its endpoints.

$\text{side 3}=\sqrt{(-9-1)^2+(-1-1)^2}=\sqrt{104}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{17} +\sqrt{117}+\sqrt{104}=25.14$

Make sure to round to places after the decimal.

Report an Error

Example Question #78 : Triangles

A triangle is defined by the following points on a coordinate plane: (1, -2), (2, -5), (-3, -3) .

What is the perimeter of the triangle?

Possible Answers:

17.89

11.41

12.67

10.51

Correct answer:

12.67

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(1, -2)\text{ and }(2, -5)$ as its endpoints.

$\text{side 1}=\sqrt{(2-1)^2+(-5-(-2))^2}=\sqrt{10}$

The second side of the triangle is the line segment that has $(2, -5)\text{ and }(-3, -3)$ as its endpoints.

$\text{side 2}=\sqrt{(-3-2)^2+(-3-(-5))^2}=\sqrt{29}$

The third side of the triangle is the line segment that has $(1, -2)\text{ and }(-3, -3)$ as its endpoints.

$\text{side 3}=\sqrt{(-3-1)^2+(-3-(-2))^2}=\sqrt{17}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{10} +\sqrt{29}+\sqrt{17}=12.67$

Make sure to round to places after the decimal.

Report an Error

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Joseph
Certified Tutor

Brown University, Bachelor of Science, Education.

View Tutors

William M.
Certified Tutor

Luther College, Bachelor in Arts, Mathematics. Northern Illinois University, Master of Arts Teaching, Mathematics Teacher Edu...

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Chicago, French Tutors in Seattle, GRE Tutors in Boston, SSAT Tutors in Boston, Chemistry Tutors in Los Angeles, Chemistry Tutors in Boston, SSAT Tutors in Miami, English Tutors in Philadelphia, French Tutors in Philadelphia, Algebra Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in New York City, ISEE Courses & Classes in Atlanta, SSAT Courses & Classes in Houston, SSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Phoenix, GRE Courses & Classes in Chicago, MCAT Courses & Classes in Chicago, SAT Courses & Classes in Washington DC, ISEE Courses & Classes in Washington DC, SAT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in Phoenix, SAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Washington DC, LSAT Test Prep in Washington DC, SSAT Test Prep in Phoenix, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Seattle, ACT Test Prep in Philadelphia, GMAT Test Prep in Phoenix, SSAT Test Prep in Chicago

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #71 : Triangles

Example Question #14 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #72 : Triangles

Example Question #73 : Triangles

Example Question #512 : Intermediate Geometry

Example Question #513 : Intermediate Geometry

Example Question #514 : Intermediate Geometry

Example Question #515 : Intermediate Geometry

Example Question #77 : Triangles

Example Question #78 : Triangles

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: