Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

Right Triangle with GREATEST AREA

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 347
Joined: Mon Aug 04, 2008 1:42 pm
Thanked: 1 times
by Stockmoose16 » Wed Oct 22, 2008 12:08 pm
I was doing an MGMAT challenge question, and I came across the following statement:

The right triangle with the largest area will be an isosceles right triangle (where both the base and height are of equal length).

This doesn't make sense. A 30-60-90 right triangle would have an area of (X^2 * sqrt 3)/2, which is clearly greater than an isoceles right triangle (45-45-90), which would have an area of just (x^2)/2

Can anyone explain?
Top
Join the discussion
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 458
Joined: Sun Aug 31, 2008 10:44 amFollowed by: 1 member
Thanked: 3 times

by gmat009 » Wed Oct 22, 2008 12:15 pm
30-60-90 right triangle

sides will be x:(sqrt 3)x:2x

A1= 1/2 *((sqrt 3)x)*x

45-45-90

sides will be x:x:((sqrt 2)x)

A2= 1/2 *x*x

A1>A2
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 347
Joined: Mon Aug 04, 2008 1:42 pm
Thanked: 1 times

by Stockmoose16 » Wed Oct 22, 2008 12:20 pm
gmat009 wrote:30-60-90 right triangle

sides will be x:(sqrt 3)x:2x

A1= 1/2 *((sqrt 3)x)*x

45-45-90

sides will be x:x:((sqrt 2)x)

A2= 1/2 *x*x

A1>A2
That's the same thing I showed above.

For A1: 1/2 * (sq rt 3 * X) *X = (X^2 * sqrt 3)/ 2, which would certainly be GREATER THAN A2.

According to the MGMAT question, ISOCELES TRIANGLES have the greatest area of all right triangles. You just proved that 30-60-90 triangles have the greatest area of all right triangles.
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 347
Joined: Mon Aug 04, 2008 1:42 pm
Thanked: 1 times

Re: Right Triangle with GREATEST AREA

by Stockmoose16 » Wed Oct 22, 2008 12:36 pm
Stockmoose16 wrote:I was doing an MGMAT challenge question, and I came across the following statement:

Given a hypotenuse, The right triangle with the largest area will be an isosceles right triangle (where both the base and height are of equal length).

This doesn't make sense. A 30-60-90 right triangle would have an area of (X^2 * sqrt 3)/2, which is clearly greater than an isoceles right triangle (45-45-90), which would have an area of just (x^2)/2

Can anyone explain?
Top
Join the discussion
User avatar
Legendary Member
Posts: 871
Joined: Wed Aug 13, 2008 7:48 am
Thanked: 48 times

by stop@800 » Wed Oct 22, 2008 10:19 pm
we are comparing in the incorrects :)


As we are changing base and height, we need ot keep hyp same


the 30 60 90 will be (order P B H)
1 sqrt(3) 2


the 45 90 45 will be
1 1 sqrt(2)
multiply all by sqrt(2)
so we have

sqrt(2) sqrt(2) 2



now compare the areas
1 sqrt(3) 2
it will be
sqrt(3) / 2 = 1.73/2


and for
sqrt(2) sqrt(2) 2

it will be
sqrt(2) * sqrt(2) /2
= 1


so definitely 45 45 90 is greater

Hope this helps

The modified question also contains given a hyp
Top
Join the discussion