We are open Saturday and Sunday!

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 #1 : Triangles

An isosceles triangle has a base of $12\ cm$ and an area of $42\ cm^{2}$ . What must be the height of this triangle?

Possible Answers:

$9\ cm$

$6\ cm$

$7\ cm$

$8\ cm$

$10\ cm$

Correct answer:

$7\ cm$

Explanation:

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

$6x=42$

$x=7$

Report an Error

Example Question #1 : Triangles

An isosceles triangle has a perimeter of . If the base of the triangle is two less than two times the length of each leg, what is the height of the triangle?

Possible Answers:

3.32

4.82

The height of the triangle cannot be determined with the given information.

3.11

Correct answer:

3.32

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be 2x-2 .

Use the information given about the perimeter to solve for .

x+x+2x-2=22

4x-2=22

4x=24

x=6

Plug this value in to find the length of the base.

$\text{Length of Base}=2(6)-2=10$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{6^2-5^2}=\sqrt{11}=3.32$

Make sure to round to places after the decimal.

Report an Error

Example Question #1 : Acute / Obtuse Isosceles Triangles

An isosceles triangle has a perimeter of . If the base of the triangle is less than three times the length of a leg, what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be 3x-18 .

Use the information given about the perimeter to solve for .

x+x+3x-18=32

5x-18=32

5x=50

x=10

Plug this value in to find the length of the base.

$\text{Length of Base}=3(10)-18=12$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{10^2-6^2}=\sqrt{64}=8$

Make sure to round to places after the decimal.

Report an Error

Example Question #3 : Triangles

An isosceles triangle has a perimeter of . If the length of the base is one less than twice the length of a leg, what is the height of the triangle?

Possible Answers:

2.90

1.29

2.44

2.18

Correct answer:

2.18

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be 2x-1 .

Use the information given about the perimeter to solve for .

x+x+2x-1=19

4x-1=19

4x=20

x=5

Plug this value in to find the length of the base.

$\text{Length of Base}=2(5)-1=9$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{5^2-4.5^2}=\sqrt{4.75}=2.18$

Make sure to round to places after the decimal.

Report an Error

Example Question #1 : Triangles

An isosceles triangle has a perimeter of . If the length of the base is fourteen less than three times the length of a leg, what is the height of the triangle?

Possible Answers:

4.93

5.66

5.89

5.09

Correct answer:

5.66

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be 3x-14 .

Use the information given about the perimeter to solve for .

x+x+3x-14=16

5x-14=16

5x=30

x=6

Plug this value in to find the length of the base.

$\text{Length of Base}=3(6)-14=4$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{6^2-2^2}=\sqrt{32}=5.66$

Make sure to round to places after the decimal.

Report an Error

Example Question #1 : Acute / Obtuse Isosceles Triangles

An isosceles triangle has a perimeter of . If the length of the base is two less than one-third of the length of a leg, what is the height of the triangle?

Possible Answers:

8.19

8.99

8.82

9.02

Correct answer:

8.99

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be $\frac{1}{3}x-2$ .

Use the information given about the perimeter to solve for .

$x+x+\frac{1}{3}x-2=19$

$\frac{7}{3}x-2=19$

$\frac{7}{3}x=21$

x=9

Plug this value in to find the length of the base.

$\text{Length of Base}=\frac{1}{3}(9)-2=1$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{9^2-(\frac{1}{2})^2}=\sqrt{80.75}=8.99$

Make sure to round to places after the decimal.

Report an Error

Example Question #6 : Triangles

An isosceles triangle has a perimeter of . If the length of the base is ten less than twice the length of a leg, what is the height of the triangle?

Possible Answers:

9.87

10.12

9.75

8.90

Correct answer:

9.75

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be 2x-10 .

Use the information given about the perimeter to solve for .

x+x+2x-10=38

4x-10=38

4x=48

x=12

Plug this value in to find the length of the base.

$\text{Length of Base}=2(12)-10=14$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{12^2-7^2}=\sqrt{95}=9.75$

Make sure to round to places after the decimal.

Report an Error

Example Question #7 : Triangles

An isosceles triangle has a perimeter of . If the length of the base is four more than one-third of the length of a leg, what is the height of the triangle?

Possible Answers:

1.97

1.20

1.59

1.66

Correct answer:

1.66

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be $\frac{1}{3}x+4$ .

Use the information given about the perimeter to solve for .

$x+x+\frac{1}{3}x+4=11$

$\frac{7}{3}x+4=11$

$\frac{7}{3}x=7$

x=3

Plug this value in to find the length of the base.

$\text{Length of Base}=\frac{1}{3}(3)+4=5$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{3^2-(\frac{5}{2})^2}=\sqrt{2.75}=1.66$

Make sure to round to places after the decimal.

Report an Error

Example Question #8 : Triangles

The perimeter of an isosceles triangle is . If the length of the base is five more than one-fourth the length of a leg, what is the height of the triangle?

Possible Answers:

18.45

15.20

19.36

19.01

Correct answer:

19.36

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be $\frac{1}{4}x+5$ .

Use the information given about the perimeter to solve for .

$x+x+\frac{1}{4}x+5=50$

$\frac{9}{4}x+5=50$

$\frac{9}{4}x=45$

x=20

Plug this value in to find the length of the base.

$\text{Length of Base}=\frac{1}{4}(20)+5=10$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{20^2-5^2}=\sqrt{375}=19.36$

Make sure to round to places after the decimal.

Report an Error

Example Question #1 : Triangles

The perimeter of an isosceles triangle is . If the length of the base is ten more than one-eighth the length of a leg, what is the height of the triangle?

Possible Answers:

15.28

14.83

13.41

10.21

Correct answer:

14.83

Explanation:

First, find the lengths of the triangle.

Let be the length of each leg. Then, the length of the base must be $\frac{1}{8}x+10$ .

Use the information given about the perimeter to solve for .

$x+x+\frac{1}{8}x+10=44$

$\frac{17}{8}x+10=44$

$\frac{17}{8}x=34$

x=16

Plug this value in to find the length of the base.

$\text{Length of Base}=\frac{1}{8}(16)+10=12$

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

Thus, we can use the Pythagorean Theorem to find the length of the height.

$\text{Height}=\sqrt{\text{leg}^2-\text{half of base}^2}$

Plug in the given values to find the height of the triangle.

$\text{Height}=\sqrt{16^2-6^2}=\sqrt{220}=14.83$

Make sure to round to places after the decimal.

Report an Error

View Tutors

George
Certified Tutor

Pensacola State College, Bachelor in Arts, Mathematics.

View Tutors

Krittika
Certified Tutor

University of Dhaka, Master's/Graduate, Statistics. University of Waterloo, Master's/Graduate, Biostatistics.

View Tutors

Jordan
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Physics. University of Maryland-College Park, Bachelor in Arts, Ger...

All Intermediate Geometry Resources

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

Popular Subjects

SSAT Tutors in Los Angeles, ISEE Tutors in Seattle, GRE Tutors in Denver, MCAT Tutors in Phoenix, Math Tutors in Washington DC, French Tutors in Seattle, Chemistry Tutors in Atlanta, Computer Science Tutors in Washington DC, Math Tutors in San Francisco-Bay Area, Algebra Tutors in Atlanta

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, Spanish Courses & Classes in Atlanta, MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Los Angeles, GMAT Courses & Classes in Washington DC, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Phoenix, LSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Denver, SAT Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Washington DC, GMAT Test Prep in New York City, LSAT Test Prep in Phoenix, GMAT Test Prep in San Diego, GRE Test Prep in Boston, ISEE Test Prep in Boston, GRE Test Prep in Chicago, GRE Test Prep in New York City, GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in San Diego

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 #1 : Triangles

Example Question #1 : Triangles

Example Question #1 : Acute / Obtuse Isosceles Triangles

Example Question #3 : Triangles

Example Question #1 : Triangles

Example Question #1 : Acute / Obtuse Isosceles Triangles

Example Question #6 : Triangles

Example Question #7 : Triangles

Example Question #8 : Triangles

Example Question #1 : Triangles

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: