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 →

Geometry

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Tue Aug 26, 2008 1:09 am
Thanked: 2 times
by chayanika » Thu Aug 28, 2008 9:46 am
If a. b, c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is:
1)equilateral
2)isosceles
3)right angled
4)obtuse angled

Can someone help me to solve this?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 105
Joined: Tue Jul 15, 2008 7:03 pm
Thanked: 5 times

by pre-gmat » Thu Aug 28, 2008 10:49 am
It should be equilateral triangle. Try putting in the values and check it.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 33
Joined: Mon Aug 04, 2008 6:52 am
Thanked: 2 times

by bomond » Thu Aug 28, 2008 11:03 am
Yes, there is easy way to solve this problem.

Multiply both side by 2

2a2+2b2+2c2=2bc+2ca+2ab
a2-2ab+b2+a2-2ca+c2+b2-2bc+c2=0
(a-b)^2+(a-c)^2+(b-c)^2=0
Each of them is >=0
So, a-b=0 a-c=0 b-c=0 =>a=b=c

Answer is equilateral
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 132
Joined: Fri Sep 05, 2008 10:19 pm
Location: Bangladesh
Thanked: 1 times

by rabab » Wed Sep 10, 2008 11:12 am
bomond wrote: (a-b)^2+(a-c)^2+(b-c)^2=0
Each of them is >=0
i don't get this part. how come each of them is greater than= 0?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Wed Sep 10, 2008 12:46 pm
rabab wrote:
bomond wrote: (a-b)^2+(a-c)^2+(b-c)^2=0
Each of them is >=0
i don't get this part. how come each of them is greater than= 0?
Anything squared will be >= 0.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1