We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Acute / Obtuse 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 #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

For the triangle below, the perimeter is . Find the value of .

Possible Answers:

Correct answer:

Explanation:

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is 2x-5 also.

Now, use the information given about the perimeter to set up an equation to solve for . The sum of all the sides will give the perimeter.

2x-5+2x-5+x=40

5x-10=40

5x=50

x=10

Report an Error

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Find the value of if the perimeter is .

Possible Answers:

Correct answer:

Explanation:

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is x+3 also.

Now, use the information given about the perimeter to set up an equation to solve for . The sum of all the sides will give the perimeter.

x+3+x+3+x=24

3x+6=24

3x=18

x=6

Report an Error

Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Find the value of if the perimeter is .

Possible Answers:

Correct answer:

Explanation:

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is 2x-2 also.

Now, use the information given about the perimeter to set up an equation to solve for . The sum of all the sides will give the perimeter.

2x-2+2x-2+3x-6=39

7x-10=39

7x=49

x=7

Report an Error

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

An acute isosceles triangle has an area of square units and a base with length . Find the perimeter of this triangle.

Possible Answers:

$\sqrt{73}+8$

$2\sqrt{73} +6$

$\sqrt{73}+6$

$2\sqrt{73}+8$

Correct answer:

$2\sqrt{73} +6$

Explanation:

To solve this problem, first work backwards using the formula:

$Area=\frac{b\cdot h}{2}$

Plugging in the given information and solving for height.

$24=\frac{6h}{2}$

$24\times2=6h$

48=6h

$h=\frac{48}{6}=8$

Now that you've found the height of the triangle, use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle.

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of 3, 8 and c^2 .

Thus, the solution is:
3^2+8^2=c^2
9+64=c^2
73=c^2

$c=\sqrt{73}$

In this problem, the isosceles triangle will have two sides with the length of $\sqrt{73}$ and one side length of . Therefore, the perimeter is: $2\sqrt{73}+6$

Report an Error

Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

A scalene triangle has sides with lengths of $\frac{3}{4}$ foot, $\frac{1}{4}$ foot, and $\frac{2}{6}$ foot. Find the perimeter of the the triangle (in inches).

Possible Answers:

18in

16in

12in

24in

Correct answer:

16in

Explanation:

To solve this problem, first convert each of the fractions from feet to inches.

$\frac{3}{4}=\frac{9}{12}=9$ inches

$\frac{1}{4}=\frac{3}{12}=3$ inches

$\frac{2}{6}=\frac{4}{12}=4$ inches

The perimeter of the triangle must equal 9+3+4=16

Report an Error

Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

An acute triangle has side lengths of and . The hypotenuse of the triangle is not . Find the perimeter of this triangle.

Possible Answers:

$3\sqrt{41}$

$\sqrt{41}+27$

$3\sqrt{41}+27$

Correct answer:

$3\sqrt{41}+27$

Explanation:

Since the two side lengths provided in the question are not the hypotenuse, first use the Pythagorean Theorem to find the length of the third side.

a^2+b^2=c^2

12^2+15^2=c^2

144+225=c^2

c^2=369

$c=\sqrt{369}=\sqrt{9}\sqrt{41}=3\sqrt{41}$

The perimeter is equal to a+b+c .

$12+15+3\sqrt{41}$

$3\sqrt{41}+27$

Report an Error

Example Question #4 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Inter_geo_tri_series_

Find the perimeter of the triangle shown above.

Possible Answers:

$4.5+\sqrt{26.5}in$

$\sqrt{26.5}in$

$\sqrt{26.5+7}in$

$7+\sqrt{26.5}in$

Correct answer:

$7+\sqrt{26.5}in$

Explanation:

Since the two side lengths provided in the question are not the hypotenuse, first use the Pythagorean Theorem to find the length of the third side.

a^2+b^2=c^2

2.5^2+4.5^2=c^2

6.25+20.25=c^2

c^2=26.5

$c=\sqrt{26.5}$

Perimeter is equal to a+b+c .

$2.5+4.5+\sqrt{26.5}=7+ \sqrt{26.5}$

Report an Error

Example Question #5 : How To Find The Perimeter Of An Acute / Obtuse Triangle

An obtuse Isosceles triangle has an area of square units and a base with length . Find the perimeter of this triangle.

Possible Answers:

$4+\sqrt{5}$

$8+8\sqrt{5}$

$8+2\sqrt{5}$

$4\sqrt{5}$

Correct answer:

$8+8\sqrt{5}$

Explanation:

To solve this solution, first work backwards using the formula: $Area=\frac{b\cdot h}{2}$

$32=\frac{8h}{2}$

8h=64

h=8

Now that you've found the height of the triangle, use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle.

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of 4,8 and c^2 .

Thus, the solution is:
4^2+8^2=c^2

16+64=c^2

c^2=80

$c=\sqrt{80}=4\sqrt{5}$

In this problem, the isosceles triangle will have two sides with the length of $4\sqrt{5}$ and one side length of . Therefore, the perimeter is: $8+8\sqrt{5}$ .

Report an Error

Example Question #6 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Inter_geo_tri_series_

Find the perimeter of the acute isosceles triangle shown above. Note, the triangle has a base of and height of .

Possible Answers:

$14\sqrt{449}$

$14+2\sqrt{449}$

$14+\sqrt{449}$

$\sqrt{449}$

Correct answer:

$14+2\sqrt{449}$

Explanation:

Use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle.

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of 7,20 and c^2 .

Thus, the solution is:
7^2+20^2=c^2

49+400=c^2

c^2=449

$c=\sqrt{449}$

In this problem, the isosceles triangle will have two sides with the length of $\sqrt{449}$ and one side length of . Therefore, the perimeter is: $14+2\sqrt{449}$ .

Report an Error

Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

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

Possible Answers:

22.4

24.5

30.7

25.3

Correct answer:

22.4

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, where the long leg is the length of the short leg times $\sqrt3$ and the hypotenuse is two times the length of the short side. We can find out that the height of the triangle is since it is the short leg and the hypotenuse is .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $6, 6, \text{ and }6\sqrt3$ .

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

$\text{Perimeter}=6+6+6\sqrt3=22.4$

Report an Error

View Tutors

Om
Certified Tutor

Pune University India, Bachelor of Science, Physics. CUNY Graduate School and University Center, Doctor of Philosophy, Nuclea...

View Tutors

Katherine
Certified Tutor

Grand Canyon University, Bachelor in Arts, English.

View Tutors

Elisabeth
Certified Tutor

The Texas A&M University System Office, Bachelor of Science, Social Work. National University, Master of Science, Applied Beh...

All Intermediate Geometry Resources

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

Popular Subjects

Statistics Tutors in Phoenix, ACT Tutors in New York City, Reading Tutors in San Diego, Statistics Tutors in New York City, Physics Tutors in Philadelphia, Calculus Tutors in Los Angeles, Calculus Tutors in Houston, ISEE Tutors in San Francisco-Bay Area, MCAT Tutors in San Francisco-Bay Area, Math Tutors in Miami

Popular Courses & Classes

GMAT Courses & Classes in San Diego, SSAT Courses & Classes in Seattle, Spanish Courses & Classes in Boston, LSAT Courses & Classes in Boston, GMAT Courses & Classes in Washington DC, ISEE Courses & Classes in Boston, SAT Courses & Classes in Boston, SSAT Courses & Classes in Phoenix, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Denver

Popular Test Prep

LSAT Test Prep in Philadelphia, SSAT Test Prep in Philadelphia, SAT Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, SAT Test Prep in Boston, SAT Test Prep in Houston, SSAT Test Prep in New York City, ISEE Test Prep in Los Angeles, GMAT Test Prep in San Diego, GRE 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 : Acute / Obtuse Triangles

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #3 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #4 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #5 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #6 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: