Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : Properties of Triangles

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

Possible Answers:

$40\textup { miles}$

$10\textup { miles}$

$60\textup { miles}$

$30\textup { miles}$

$50\textup { miles}$

Correct answer:

$50\textup { miles}$

Explanation:

The distances when put together create a right triangle.

The distance between them will be the hypotenuse or the diagonal side.

You use Pythagorean Theorem or $a^{2}+b^{2}=c^{2}$ to find the length.

So you plug and for and which gives you,

$900+1600=c^{2}$ or $2500=c^{2}$ .

Then you find the square root of each side and that gives you your answer of c=50 .

Report an Error

Example Question #1 : How To Find The Height Of A Right Triangle

If the hypotenuse of a right triangle is 20, and one of the legs is 12, what is the value of the other leg?

Possible Answers:

Correct answer:

Explanation:

The triangle in this problem is a variation of the 3, 4, 5 right triangle. However, it is 4 times bigger. We know this because $5\cdot4=20$ (the length of the hypotenuse) and $3\cdot4=12$ (the length of one of the legs).

Therefore, the length of the other leg will be equal to:

$4\cdot4=16$

Report an Error

Example Question #33 : Properties Of Triangles

A given right triangle has a base of length 9cm and a total area of $45cm^{2}$ . What is the height of the right triangle?

Possible Answers:

8cm

9cm

5cm

Not enough information provided

10cm

Correct answer:

10cm

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

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

2A=bh

$\frac{2A}{b}=h$

Plugging in our values for and :

$\frac{2(45cm^{2})}{9cm}=h$

$\frac{90cm^{2}}{9cm}=h$

10cm=h

Report an Error

Example Question #34 : Properties Of Triangles

A given right triangle has a base length of 10cm and a total area of $100cm^{2}$ . What is the height of the triangle?

Possible Answers:

Not enough information provided

20cm

5cm

10cm

90cm

Correct answer:

20cm

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

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

2A=bh

$\frac{2A}{b}=h$

Plugging in our values for and :

$\frac{2(100cm^{2})}{10cm}=h$

$\frac{200cm^{2}}{10cm}=h$

20cm=h

Report an Error

Example Question #31 : Properties Of Triangles

A given right triangle has a hypotenuse of 30cm and a total area of $200cm^{2}$ . What is the height of the triangle?

Possible Answers:

10cm

25cm

30.77cm

20cm

Not enough information provided

Correct answer:

Not enough information provided

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

However, we have not been given a base or leg length for the right triangle, only the length of the hypotenuse and the area. We therefore do not have enough information to solve for the height .

Report an Error

Example Question #701 : Ssat Upper Level Quantitative (Math)

The area of a right triangle is 100m^2 . If the base of the triangle is 25m , what is the height, in meters?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=25$

$\text{Area}=100$

$100=\frac{25\times height}{2}$

Now, solve for the height.

$25\times height=200$

height=8

Report an Error

Example Question #37 : Properties Of Triangles

The area of a right triangle is 45m^2 , and the base is 15m . What is the height, in meters?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=15$

$\text{Area}=45$

$45=\frac{15\times height}{2}$

Now, solve for the height.

$15\times height=90$

height=6

Report an Error

Example Question #38 : Properties Of Triangles

The area of a right triangle is $50\textup{ in}^2$ . If the base of the triangle is $10\textup{ in}$ , what is the length of the height, in inches?

Possible Answers:

Correct answer:

Explanation:

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=10$

$\text{Area}=50$

$50=\frac{10\times height}{2}$

Now, solve for the height.

$10\times height=100$

height=10

Report an Error

Example Question #1 : How To Find The Area Of A Right Triangle

Right Triangle A has hypotenuse 25 inches and one leg of length 24 inches; Right Triangle B has hypotenuse 15 inches and one leg of length 9 inches; Rectangle C has length 16 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the width of Rectangle C?

Possible Answers:

$17 \frac{1}{4} \textrm{ in}$

$6 \frac{7}{8} \textrm{ in}$

$10 \frac{1}{2} \textrm{ in}$

$8 \frac{5}{8} \textrm{ in}$

$14\frac{7}{8} \textrm{ in}$

Correct answer:

$8 \frac{5}{8} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. In each case, we know the length of one leg and the hypotenuse, so we need to apply the Pythagorean Theorem to find the second leg, then take half the product of the legs:

Right Triangle A:

The length of the second leg is

$\sqrt{25^{2} -24 ^{2}} = \sqrt{625 - 576} = \sqrt{49} = 7$ inches.

The area is

$\frac{1}{2} \times 7 \times 24 = 84$ square inches.

Right Triangle B:

The length of the second leg is

$\sqrt{15^{2} -9 ^{2}} = \sqrt{225 - 81} = \sqrt{144} = 12$ inches.

The area is

$\frac{1}{2} \times 9 \times 12 = 54$ square inches.

The sum of the areas is 84 + 54 = 138 square inches.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $138 \div 16 = 8 \frac{5}{8}$ inches.

Report an Error

Example Question #2 : How To Find The Area Of A Right Triangle

Right Triangle A has legs of lengths 10 inches and 14 inches; Right Triangle B has legs of length 20 inches and 13 inches; Rectangle C has length 30 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the height of Rectangle C?

Possible Answers:

$10 \textrm{ in}$

$5 \textrm{ in}$

$6 \frac{2}{3} \textrm{ in}$

$13\frac{1}{3} \textrm{ in}$

Insufficient information is given to determine the height.

Correct answer:

$6 \frac{2}{3} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. The area of Right Triangle A is equal to $\frac{1}{2} \times 10 \times 14 = 70$ square inches; that of Right Triangle B is equal to $\frac{1}{2} \times 20 \times 13 = 130$ square inches. The sum of the areas is 70 + 130 = 200 square inches, which is the area of Rectangle C.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $200 \div 30 = 6 \frac{2}{3}$ inches.

Report an Error

View SSAT- Upper Level Tutors

Brooke
Certified Tutor

New York University, Bachelor in Arts, Drama and Dance Teacher Education. Georgia State University, Master of Arts, Communica...

View SSAT- Upper Level Tutors

Carneta
Certified Tutor

Langston University, Bachelor in Arts, Theater Arts.

View SSAT- Upper Level Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Philadelphia, SSAT Tutors in Dallas Fort Worth, French Tutors in San Diego, Computer Science Tutors in Atlanta, Statistics Tutors in San Diego, Chemistry Tutors in Atlanta, SSAT Tutors in San Francisco-Bay Area, GRE Tutors in Phoenix, English Tutors in San Diego, ACT Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, GRE Courses & Classes in Los Angeles, SSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Houston, LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in Washington DC, ISEE Courses & Classes in Boston, GRE Courses & Classes in Seattle, Spanish Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in Los Angeles, SAT Test Prep in Denver, MCAT Test Prep in Philadelphia, ACT Test Prep in New York City, SSAT Test Prep in Houston, LSAT Test Prep in Chicago, GRE Test Prep in Denver, SAT Test Prep in Phoenix, ISEE Test Prep in Washington DC, MCAT 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

SSAT Upper Level Math : Properties of Triangles

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #11 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

Example Question #1 : How To Find The Height Of A Right Triangle

Example Question #33 : Properties Of Triangles

Example Question #34 : Properties Of Triangles

Example Question #31 : Properties Of Triangles

Example Question #701 : Ssat Upper Level Quantitative (Math)

Example Question #37 : Properties Of Triangles

Example Question #38 : Properties Of Triangles

Example Question #1 : How To Find The Area Of A Right Triangle

Example Question #2 : How To Find The Area Of A Right Triangle

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: