Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to find the perimeter of a 45/45/90 right isosceles triangle

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 #1 : Isosceles Triangles

What is the perimeter of an isosceles right triangle with an hypotenuse of length $20\:cm$ ?

Possible Answers:

$10\sqrt{2} + 20\:cm$

$80\sqrt{2}\:cm$

$20\sqrt{2}+20\:cm$

$60\:cm$

$40\sqrt{2}\:cm$

Correct answer:

$20\sqrt{2}+20\:cm$

Explanation:

Your right triangle is a 45-45-90 triangle. It thus looks like this:

_tri41

Now, you know that you also have a reference triangle for 45-45-90 triangles. This is:

Triangle454590

This means that you can set up a ratio to find . It would be:

$\frac{x}{1}=\frac{20}{\sqrt{2}}$

Your triangle thus could be drawn like this:

_tri42

Now, notice that you can rationalize the denominator of $\frac{20}{\sqrt{2}}$ :

$\frac{20}{\sqrt{2}} = \frac{20}{\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}=\frac{20\sqrt{2}}{2}=10\sqrt{2}$

Thus, the perimeter of your figure is:

$10\sqrt{2} + 10\sqrt{2} + 20 = 20\sqrt{2}+20\:cm$

Report an Error

Example Question #2 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of an isosceles right triangle with an area of $72x^2\:in^2$ ?

Possible Answers:

$36x^2\sqrt{2}\:in$

$36x\sqrt{2}\:in$

$144x^2\:in$

$144x^2 + 12\sqrt{2}\:in$

$24x+12x\sqrt{2}\:in$

Correct answer:

$24x+12x\sqrt{2}\:in$

Explanation:

Recall that an isosceles right triangle is also a 45-45-90 triangle. Your reference figure for such a shape is:

Triangle454590 or _tri51

Now, you know that the area of a triangle is:

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

For this triangle, though, the base and height are the same. So it is:

$A=\frac{1}{2}x^2$

Now, we have to be careful, given that our area contains . Let's use , for "side length":

$72x^2=\frac{1}{2}s^2$

s^2=144x^2

Thus, $s=12x\:in$ . Now based on the reference figure above, you can easily see that your triangle is:

_tri71

Therefore, your perimeter is:

$12x+12x+12x\sqrt{2} = 24x+12x\sqrt{2}\:in$

Report an Error

Example Question #202 : Plane Geometry

A tree is feet tall and is planted in the center of a circular bed with a radius of feet. If you want to stabalize the tree with ropes going from its midpoint to the border of the bed, how long will each rope measure?

Possible Answers:

24.5 ft

15 ft

13 ft

19 ft

12 ft

Correct answer:

13 ft

Explanation:

This is a right triangle where the rope is the hypotenuse. One leg is the radius of the circle, 5 feet. The other leg is half of the tree's height, 12 feet. We can now use the Pythagorean Theorem a^2+b^2=c^2 giving us 5^2+12^2=169 . If c^2=169 then $c=\sqrt{169}=13$ .

Report an Error

Example Question #141 : Triangles

An isosceles right triangle has a hypotenuse of length . What is the perimeter of this triangle, in terms of ?

Possible Answers:

$x+ x\sqrt 2$

$\frac{4}{3}x$

$\frac{2}{3}x$

$x+ x\sqrt3$

Correct answer:

$x+ x\sqrt 2$

Explanation:

The ratio of sides to hypotenuse of an isosceles right triangle is always $x: x: x\sqrt2$ . With this in mind, setting as our hypotenuse means we must have leg lengths equal to:

$\frac{x}{\sqrt2} = \frac{x\sqrt2}{2}$

Since the perimeter has two of these legs, we just need to multiply this by and add the result to our hypothesis:

$P\Delta = x + 2\left(\frac{x\sqrt2}{2}\right) = x+ x\sqrt2$

So, our perimeter in terms of is:

$x+ x\sqrt 2$

Report an Error

View ACT Math Tutors

Shane
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Engineering, General.

View ACT Math Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

View ACT Math Tutors

Jonathan
Certified Tutor

University of Illinois at Chicago, Bachelor in Arts, Criminal Justice. Syracuse University, Masters in Business Administratio...

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

MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Los Angeles, Spanish Courses & Classes in Phoenix, SAT Courses & Classes in Los Angeles, SSAT Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Philadelphia

Popular Test Prep

ISEE Test Prep in Chicago, SSAT Test Prep in Boston, ACT Test Prep in Philadelphia, MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Dallas Fort Worth, SSAT Test Prep in Houston, SAT Test Prep in Chicago, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Phoenix, ACT Test Prep in Dallas Fort Worth

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 : How to find the perimeter of a 45/45/90 right isosceles triangle

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Isosceles Triangles

Example Question #2 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Example Question #202 : Plane Geometry

Example Question #141 : Triangles

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: