BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

45-45-90 triangle - radicals question

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sun Nov 02, 2008 3:55 pm
by damrkstr » Sun Nov 02, 2008 5:13 pm
The perimeter of a certain isosceles right triangle is 16 + 16√2.
What is the length of the hypotenuse of the triangle?

I tried solving it setting x + x + x√2 = 16 + 16√2 but am not solving it correctly. Could someone help me out with the best way to solve the problem?

The answer was supposed to be 16

Thanks for your help!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Community Manager
Posts: 1049
Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members
Location: Pittsburgh, PA
Thanked: 113 times
GMAT Score:710

by dmateer25 » Sun Nov 02, 2008 5:37 pm
The equation you set up will work just fine. I think the best way to solve this using your equation is to just estimate √2 as 1.4.

x + x + 1.4x = 16 + 16(1.4)

3.4x = 38.4

x = ~11.3


The hypotenuse would be 1.4 (11.3) = ~15.82

It would be pretty clear that the answer would be 16.

Also you could do the following:

Assume that the hypotenuse is x and the sides of the triangle are x√2/2.

(x√2/2)+(x√2/2)+x=16 + 16√2
2x√2/2 + x = 16 + 16√2
x√2 + x = 16 + 16√2

x =16
x√2=16√2
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 207
Joined: Sun Mar 11, 2007 6:16 pm
Location: Mumbai
Thanked: 11 times

Re: 45-45-90 triangle - radicals question

by jimmiejaz » Wed Nov 05, 2008 4:24 am
damrkstr wrote:The perimeter of a certain isosceles right triangle is 16 + 16√2.
What is the length of the hypotenuse of the triangle?

I tried solving it setting x + x + x√2 = 16 + 16√2 but am not solving it correctly. Could someone help me out with the best way to solve the problem?

The answer was supposed to be 16

Thanks for your help!
taking ahead your approach...
we can see
x + x + x√2 = 16 + 16√2
pick numbers...
first take x=8, it gives
8+8+8√2 which is not equal to 16+16√2. hence xis not eual to 8.
now pick x=8√2
8√2+8√2+16 = 16+16√2

hence the side of the triangle is 8√2 and the hypotenuse is 16.
U arrived at the equation correctly but then had to just pick numbers.
hope it helps...
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 207
Joined: Sun Mar 11, 2007 6:16 pm
Location: Mumbai
Thanked: 11 times

Re: 45-45-90 triangle - radicals question

by jimmiejaz » Wed Nov 05, 2008 4:30 am
damrkstr wrote:The perimeter of a certain isosceles right triangle is 16 + 16√2.
What is the length of the hypotenuse of the triangle?

I tried solving it setting x + x + x√2 = 16 + 16√2 but am not solving it correctly. Could someone help me out with the best way to solve the problem?

The answer was supposed to be 16

Thanks for your help!
one more simple and elegant approach.....
x+x+x√2= 16 + 16√2
2x+x√2=16(1+√2)
x√2(√2+1)=16(1+√2)
which gives x√2 = 16 or x = 8√2
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sat Nov 08, 2008 2:25 am

by stickyfingers48 » Sat Nov 08, 2008 3:01 am
2x²=y² and 2x+y=16+16√2

y=16[/list]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 59
Joined: Tue Jun 10, 2008 6:49 pm
Thanked: 2 times

Re: 45-45-90 triangle - radicals question

by cartera » Sun Nov 09, 2008 6:02 am
jimmiejaz wrote:
damrkstr wrote:The perimeter of a certain isosceles right triangle is 16 + 16√2.
What is the length of the hypotenuse of the triangle?

I tried solving it setting x + x + x√2 = 16 + 16√2 but am not solving it correctly. Could someone help me out with the best way to solve the problem?

The answer was supposed to be 16

Thanks for your help!
one more simple and elegant approach.....
x+x+x√2= 16 + 16√2
2x+x√2=16(1+√2)
x√2(√2+1)=16(1+√2)
which gives x√2 = 16 or x = 8√2
x = 8√2 is not 16 and also, how did you turn 2x+x√2 into x√2(√2+1)?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 30
Joined: Sun Oct 26, 2008 5:42 pm
Thanked: 5 times

Re: 45-45-90 triangle - radicals question

by Ossa » Sun Nov 09, 2008 5:04 pm
cartera wrote:
jimmiejaz wrote:
damrkstr wrote:The perimeter of a certain isosceles right triangle is 16 + 16√2.
What is the length of the hypotenuse of the triangle?

I tried solving it setting x + x + x√2 = 16 + 16√2 but am not solving it correctly. Could someone help me out with the best way to solve the problem?

The answer was supposed to be 16

Thanks for your help!
one more simple and elegant approach.....
x+x+x√2= 16 + 16√2
2x+x√2=16(1+√2)
x√2(√2+1)=16(1+√2)
which gives x√2 = 16 or x = 8√2
x = 8√2 is not 16 and also, how did you turn 2x+x√2 into x√2(√2+1)?
Hi,
Let me answer the second part of your question:
Remembering that √2*√2=2, then 2x=(√2*√2)x
Accordingly 2x+x√2=(√2*√2)x+x√2=x√2(√2+1)
Ossa Elhadary, PhD, CISA, PMP
Math Specialist
Test Prep New York
maximize your score, minimize your stress

www.testprepny.com
[email protected]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1