We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Triangles

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #73 : Right Triangles

The lengths of the sides of a right triangle are consecutive integers, and the length of the shortest side is . Which of the following expressions could be used to solve for ?

Possible Answers:

x+x-3=x

x^2+(x+2)^2=(x+4)^2

x^2+(x+1)^2=(x+2)^2

(x+2)-(x+1)=x

(x)(x+1)=(x+2)^2

Correct answer:

x^2+(x+1)^2=(x+2)^2

Explanation:

Since the lengths of the sides are consecutive integers and the shortest side is , the three sides are , (x+1) , and (x+2) .

We then use the Pythagorean Theorem:

$\newline a^2+b^2=c^2 \newline x^2+(x+1)^2=(x+2)^2$

Report an Error

Example Question #71 : Triangles

Square PQRS is on the coordinate plane, and each side of the square is parallel to either the -axis or -axis. Point has coordinates $\left ( -2,-1 \right )$ and point has the coordinates $\left ( 3,4 \right )$ .

Quantity A: $5\sqrt{2}$

Quantity B: The distance between points and

Possible Answers:

The relationship cannot be determined from the information provided.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

Correct answer:

The two quantities are equal.

Explanation:

To find the distance between points and , split the square into two 45-45-90 triangles and find the hypotenuse. The side ratio of the 45-45-90 triangle is $s:s:s\sqrt{2}$ , so if the sides have a length of 5, the hypotenuse must be $5\sqrt{2}$ .

Report an Error

Example Question #124 : Geometry

What is the diagonal of a computer screen that measures inches tall by inches wide?

Possible Answers:

18 inches

23 inches

20 inches

7 inches

17 inches

Correct answer:

17 inches

Explanation:

Plug the values into the Pythagorean Theorem

a^2 +b^2 = c^2 ,

because we are solving for the diagonal we are looking for .

8^2 + 15^2 = 289 .

$\sqrt{289} = 17$ .

Report an Error

Example Question #131 : Geometry

A right triangle has legs of length 20cm and 99 cm , what is the length of the hypotenuse?

Possible Answers:

10,201 cm

119 cm

$\sqrt{119}$

104cm

101 cm

Correct answer:

101 cm

Explanation:

To find the hypotenuse of a right triangle, use the Pythagorean Theorem and plug the leg values in for and :
$\\a^2 + b^2 = c^2 \\ \newline 20^2 + 99^2 = c^2 \\ \newline 10,201 = c^2 \\ \\ \sqrt{10,201}=\sqrt{c^2}\\ \newline 101 = c$

Report an Error

Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has a base of six and a height of eight. Using this information find the hypotenuse.

Possible Answers:

100

Correct answer:

Explanation:

This question calls for us to use the Pythagorean Theorem. This theorem has a formula of

a^2+b^2=c^2

where a and b are the sides of a right triangle, adjacent to the right angle, and c is the hypotenuse.

Given our information

$\\6^2+8^2=c^2\\ =36+64=100\\c=\sqrt{100}=10$ .

Report an Error

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has a base of seven and a height of twelve. Using this information find the hypotenuse.

Possible Answers:

$\sqrt{19}$

$\sqrt{17}$

193

$\sqrt{193}$

Correct answer:

$\sqrt{193}$

Explanation:

This question calls for us to use the Pythagorean Theorem. This theorem has a formula of

a^2+b^2=c^2

where a and b are the sides of a right triangle, adjacent to the right angle, and c is the hypotenuse.

Given our information

$\\7^2+12^2=c^2\\=49+144=193\\c=\sqrt{193}$ .

Report an Error

Example Question #132 : Geometry

Marcus Absent is marking out some lines for a large canvas tent. He paces out $15\textup{ feet}$ to the north, places a peg, then turns east and paces another $25\textup{ feet}$ to place another peg. Stopping, he realizes he has forgotten the other pegs, so he makes a beeline for his original starting point.

How many $\textup{ feet}$ does Marcus travel to get back to the pegs?

Possible Answers:

$5\sqrt{34}\textup{ feet}$

$\textup{There is not enough information to answer the question.}$

$3\sqrt{13}\textup{ feet}$

$40\textup{ feet}$

$3\sqrt{22}\textup{ feet}$

Correct answer:

$5\sqrt{34}\textup{ feet}$

Explanation:

The Pythagorean Theorem states that for any right triangle with legs and and hypotenuse :

a^2 + b^2 = c^2 .

Applying this to Marcus's steps, we know that 15^2 + 25^2 = c^2 .

Expand:

225 + 625 = 850

So, c^2 = 850 . To find , just take the square root:

$\sqrt{850} = \sqrt{25 \cdot 34} = 5\sqrt{34}$

So, Marcus travels exactly $5\sqrt{34}\textup{ feet}$ back to the start.

Report an Error

Example Question #513 : Geometry

Justin travels $15\textup{ feet}$ to the east and $20\textup{ feet}$ to the north. How far away from his starting point is he now?

Possible Answers:

$45\textup{ ft}$

$25\textup{ ft}$

$35\textup{ ft}$

$22\textup{ ft}$

$30\textup{ ft}$

Correct answer:

$25\textup{ ft}$

Explanation:

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that a^2+b^2=c^2

15^2 + 20^2 = c^2

225+400=c^2

625=c^2

25=c

Report an Error

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Susie walks north from her house to a park that is 30 meters away. Once she arrives at the park, she turns and walks west for 80 meters to a bench to feed some pigeons. She then walks north for another 30 meters to a concession stand. If Susie returns home in a straight line from the concession stand, how far will she walk from the concession stand to her house, in meters?

Possible Answers:

100

200

Correct answer:

100

Explanation:

Susie walks 30 meters north, then 80 meters west, then 30 meters north again. Thus, she walks 60 meters north and 80 meters west. These two directions are 90 degrees away from one another.

At this point, construct a right triangle with one leg that measures 60 meters and a second leg that is 80 meters.

You can save time by using the 3:4:5 common triangle. 60 and 80 are $3\cdot 20$ and $4\cdot 20$ , respectively, making the hypotenuse equal to $5\cdot 20=100$ .

We can solve for the length of the missing hypotenuse by applying the Pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

Substitute the following known values into the formula and solve for the missing hypotenuse: side .

$a= 60,\ b= 80,\ c= ?$

$(60)^{2}+(80)^{2}=c^{2}$

$3600+6400=c^{2}$

$10,000=c^{2}$

c=100

Susie will walk 100 meters to reach her house.

Report an Error

Example Question #72 : Triangles

The lengths of the sides of a triangle are consecutive odd numbers and the triangle's perimeter is 57 centimeters. What is the length, in centimeters, of its longest side?

Possible Answers:

Correct answer:

Explanation:

First, define the sides of the triangle. Because the side lengths are consecutive odd numbers, if we define the shortest side will be as , the next side will be defined as x+2 , and the longest side will be defined as x+4 . We can then find the perimeter of a triangle using the following formula:

$\text{Perimeter}=\text{side}+\text{side}+\text{side}$

Substitute in the known values and variables.

$\text{Perimeter}=x+(x+2)+(x+4)$

57=3x+6

Subtract 6 from both sides of the equation.

57-6=3x+6-6

51=3x

Divide both sides of the equation by 3.

$\frac{51}{3}=\frac{3x}{3}$

Solve.

x=17

This is not the answer; we need to find the length of the longest side, or x+4 .

$\text{Longest side}=x+4$

Substitute in the calculated value for and solve.

$\text{Longest side}=17+4$

$\text{Longest side}=21$

The longest side of the triangle is 21 centimeters long.

Report an Error

View ACT Math Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

View ACT Math Tutors

Chukwudi
Certified Tutor

University of Nigeria, Nsukka., Bachelor of Science, Biochemistry. African University of Science and Technology., Master of S...

View ACT Math Tutors

Jhemson
Certified Tutor

Batangas State University, Doctor of Philosophy, Mathematics.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Denver, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Denver, Spanish Courses & Classes in Boston, GRE Courses & Classes in Boston, MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Washington DC, MCAT Courses & Classes in Atlanta

Popular Test Prep

GMAT Test Prep in Philadelphia, MCAT Test Prep in San Diego, SAT Test Prep in San Diego, GRE Test Prep in Miami, ISEE Test Prep in San Francisco-Bay Area, MCAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Los Angeles, ISEE Test Prep in Chicago, GMAT Test Prep in New York City

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

ACT Math : Triangles

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #73 : Right Triangles

Example Question #71 : Triangles

Example Question #124 : Geometry

Example Question #131 : Geometry

Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #132 : Geometry

Example Question #513 : Geometry

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #72 : Triangles

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: