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

Redeem

Geometry Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 81
Joined: Thu May 03, 2012 1:48 pm
Thanked: 4 times

Geometry Problem

by Blue_Skies » Wed May 08, 2013 6:51 pm
Is the area of the triangle ABC more than 12 sq. units?

(1) The GCD of the sides AB and AC is 2.
(2) The LCM of the sides AB and AC is 12.

Can someone discuss the solution for this.

An important assertion given in the Solution that i saw is that maximum area of the triangle whose two sides are given is when the two given sides are at right angle to each other. Can experts comment on this.

Thanks!
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 149
Joined: Wed May 01, 2013 10:37 pm
Thanked: 54 times
Followed by:9 members

by Atekihcan » Thu May 09, 2013 12:54 am
Let us assume that we have a triangle ABC in which we know the lengths of AB and BC.
Now, let us assume BC is the base of the triangle as shown in the following diagram.
Image
In the above diagram ABC, A'BC, and A"BC are three triangles each with the same base BC and AB = A'B = A"B
Now, are of a triangle is given by (length of base)*(length of height)/2

In triangle ABC, AB is perpendicular on BC.
So, area of ABC = (AB)*(BC)/2

Now in triangles A'BC and A"BC, the heights of the triangles (Green and red) with respect base BC are clearly less than AB.

This proves that maximum area of the triangle whose two sides are given is when the two given sides are at right angle to each other.

This can be proved using trigonometry also but that is beyond the scope of GMAT.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu May 09, 2013 3:29 am
Blue_Skies wrote: An important assertion given in the Solution that i saw is that maximum area of the triangle whose two sides are given is when the two given sides are at right angle to each other. Can experts comment on this.

Thanks!
I posted an explanation here:

https://www.beatthegmat.com/area-when-si ... 86637.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1