We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to find the length of the side of a triangle

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Triangle

Which of the following could be the lengths of the three sides of a scalene triangle?

Possible Answers:

All of the other choices are possible lengths of a scalene triangle

$5,000 \textrm{ m, } 4,000 \textrm{ m, }8,000 \textrm{ m}$

$6 \textrm{ in, } 8 \textrm{ in, }10 \textrm{ in}$

$0.7 \textrm{ in, } 0.9 \textrm{ in, }1.4 \textrm{ in}$

$8 \textrm{ cm, } 9 \textrm{ cm, }10 \textrm{ cm}$

Correct answer:

All of the other choices are possible lengths of a scalene triangle

Explanation:

A scalene triangle, by definition, has sides all of different lengths. Since all of the given choices fit that criterion, the correct choice is that all can be scalene.

Report an Error

Example Question #12 : Geometry

Given $\Delta ABC$ with right angle $\angle B$ , $m \angle C = 50 ^{\circ }$ .

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is greater

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

Correct answer:

(a) is greater

Explanation:

$m \angle B = 90^{\circ}$

$m \angle C = 50 ^{\circ }$

The sum of the measures of the angles of a triangle is 180, so

$m \angle A + m \angle B + m \angle C = 180$

$m \angle A +90 + 50 = 180$

$m \angle A +140= 180$

$m \angle A +140-140= 180-140$

$m \angle A = 40^{\circ }$

$m \angle C > m \angle A$ , so the side opposite $\angle C$ , which is $\overline{AB}$ , is longer than the side opposite $\angle A$ , which is $\overline{BC}$ . This makes (a) the greater quantity.

Report an Error

Example Question #3 : How To Find The Length Of The Side Of A Triangle

Given $\Delta ABC$ with obtuse angle $\angle A$ , which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(b) is greater.

Explanation:

To compare the lengths of $\overline{AB}$ and $\overline{BC}$ from the angle measures, it is necessary to know which of their opposite angles - $\angleC$ $\angle C$ and $\angle A$ , respectively - is the greater angle. Since $\angle A$ is the obtuse angle, it has the greater measure, and $\overline{BC}$ is the longer side. This makes (b) greater.

Report an Error

Example Question #1 : How To Find The Length Of The Side Of A Triangle

$\Delta ABC$ has obtuse angle $\angle B$ ; AB = 7, BC = 24 . Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

(a) is greater.

Explanation:

Since $\angle B$ is the obtuse angle of $\Delta ABC$ ,

$\left ( AC \right )^{2} >\left ( AB \right )^{2} + \left ( BC \right )^{2} = 7^{2} + 24^{2} = 49 + 576 = 625$ .

$\left ( AC \right )^{2} > 625$ ,

$AC > \sqrt{625}$

AC >25 ,

so (a) is the greater quantity.

Report an Error

Example Question #2 : How To Find The Length Of The Side Of A Triangle

Given $\Delta ABC$ with AB = 5, BC = 12 . Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

(b) is greater.

Explanation:

Use the Triangle Inequality:

AC < AB + BC

AC < 5 + 12

AC < 17

This makes (b) the greater quantity.

Report an Error

Example Question #11 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Given $\Delta ABC$ with AB = 5, BC = 12 . Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater.

(b) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

Correct answer:

It is impossible to tell from the information given.

Explanation:

By the Converse of the Pythagorean Theorem,

$AC = \sqrt{(AB)^{2}+(BC)^{2}}= \sqrt{5^{2}+12^{2}}= \sqrt{25+144}=\sqrt{169} = 13$

if and only if $\angle B$ is a right angle.

However, if $\angle B$ is acute, then AC < 13 ; if $\angle B$ is obtuse, then AC > 13 .

Since we do not know whether $\angle B$ is acute, right, or obtuse, we cannot determine whether (a) or (b) is greater.

Report an Error

Example Question #2 : How To Find The Length Of The Side Of A Triangle

$\Delta ABC$ is acute; AB = 5, BC = 12 . Which is the greater quantity?

(a)

(b)

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

Since $\Delta ABC$ is an acute triangle, $\angle B$ is an acute angle, and

$\left ( AC \right )^{2} < \left ( AB \right )^{2} + \left ( BC \right )^{2} = 5^{2} + 12^{2} = 25 + 144 = 169$

$\left ( AC \right )^{2} < 169$ ,

$AC< \sqrt{169}$

AC < 13

(b) is the greater quantity.

Report an Error

Example Question #5 : How To Find The Length Of The Side Of A Triangle

Given: $\bigtriangleup ABC$ . $AB= AC = 12, m \angle A = 80 ^{\circ }$ . Which is the greater quantity?

(a) 18

(b)

Possible Answers:

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

Correct answer:

(a) is the greater quantity

Explanation:

Suppose there exists a second triangle $\bigtriangleup DEF$ such that DE = DF = 12 and EF = 18 . Whether $\angle D$ , the angle opposite the longest side, is acute, right, or obtuse can be determined by comparing the sum of the squares of the lengths of the shortest sides to the square of the length of the longest:

$(DE)^{2}+ (DF)^{2} = 12^{2}+ 12^{2} = 144 + 144 = 288$

$(EF) ^{2}= 18 ^{2} = 324$

$(EF) ^{2}> (DE)^{2}+ (DF)^{2}$ , making $\angle D$ obtuse, so $m \angle D > 90 ^{\circ }$ .

We know that

$AB= AC = 12, m \angle A = 80 ^{\circ }$

and

$DE = DF = 12, m \angle D > m \angle A$ .

Between $\bigtriangleup ABC$ and $\bigtriangleup DEF$ , we have two sets of congruent sides, with the included angle of the latter of greater measure than that of the former. It follows from the Side-Angle-Side Inequality (or Hinge) Theorem that between the third sides, $\overline{EF}$ is the longer. Therefore,

BC < EF = 18 .

Report an Error

View Tutors

Ana
Certified Tutor

Grand Canyon University, Bachelors, Education. Grand Canyon University, Masters, Education.

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Tutors

Ericka
Certified Tutor

Southern Nazarene University, Bachelors, Network Engineering and Management . Oklahoma State University-Main Campus, Master o...

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Denver, Statistics Tutors in Washington DC, Physics Tutors in Washington DC, SSAT Tutors in Dallas Fort Worth, SAT Tutors in Miami, SSAT Tutors in Boston, Reading Tutors in Houston, GRE Tutors in Miami, SAT Tutors in Philadelphia, SSAT Tutors in Atlanta

Popular Courses & Classes

SAT Courses & Classes in Miami, ACT Courses & Classes in Atlanta, ACT Courses & Classes in Seattle, Spanish Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Miami, ACT Courses & Classes in Houston, ISEE Courses & Classes in San Diego, GRE Courses & Classes in San Diego, ACT Courses & Classes in New York City, SAT Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in San Diego, SAT Test Prep in Seattle, ISEE Test Prep in Phoenix, LSAT Test Prep in New York City, MCAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Houston, LSAT Test Prep in Phoenix, ACT Test Prep in New York City, GMAT Test Prep in Philadelphia, ISEE 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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ISEE Upper Level Quantitative : How to find the length of the side of a triangle

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Triangle

Example Question #12 : Geometry

Example Question #3 : How To Find The Length Of The Side Of A Triangle

Example Question #1 : How To Find The Length Of The Side Of A Triangle

Example Question #2 : How To Find The Length Of The Side Of A Triangle

Example Question #11 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #2 : How To Find The Length Of The Side Of A Triangle

Example Question #5 : How To Find The Length Of The Side Of A Triangle

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: