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

Redeem

Right angle triange ques............Quite tough .Plz help

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Tue Mar 02, 2010 9:38 am
Location: India
Followed by:1 members
GMAT Score:540

Right angle triange ques............Quite tough .Plz help

by pardeep_10sharma » Sat May 22, 2010 1:18 am
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > Suare root (2)
B. {Square root( 3) }/ 2 < y < Square root (2)
C. {Square root( 2) }/ 3 < y < {Square root( 3) }/ 2
D. {Square root( 3) }/ 4 < y < {Square root( 2) }/ 3
E. y < {Square root( 3) }/ 4

Ans is :- A ............Plz help
Top
Source: — Problem Solving |
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Thu Apr 29, 2010 5:16 am

by evsistr » Sat May 22, 2010 1:51 am
The triangle is right, hence its biggest side z ought to be a hypotenuse and x and y ought to be its legs. The area of a right triangle is determined to be the half of the product of its legs: 1/2 x y = S = 1, therefore x y = 2.
We know that x < y, so we start to check the answers to find a pair of values of x and y with a product equal to 2. We're not going to check all the possible values, but we're going to check whether 2 is in the range of minimal and maximal values of x and y product. If the maximal value of such product is less than 2, then we simply cut out the option.

A. y > √2, then x ≤ √2: MAX(x y) = √2√2 = 2. O.K.!

B. √3 / 2 < y < √2, then x ≤ √3 / 2: the maximum value that can be obtained is x y = √2 √3 / 2 = √6 / 2. The root of 6 is sure to be less than 4, divided by 2 it gives a number certainly less than 2.

C. √2 / 3 < y < √3 / 2, then x ≤ √2 / 3. We act in the same way as above: x y = (√2 / 3) (√3 / 2) = √6 / 6 = 1 / √6 < 2.

D. √3 / 4 < y < √2 / 3, then x ≤ √3 / 4. We act in the same way as in B: x y = (√3 / 4) (√2 / 3) = √6 / 12 = 1 / 2√6 < 2.

E. y < √3 / 4, assuming y to be the closest number to √3 / 4, we get that maximal x has also to be the closest number to √3 / 4, hence their maximal product is the closest number to (√3 / 4)(√3 / 4) = 3/16, which is no doubt less than 2.
Top
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Tue Mar 02, 2010 9:38 am
Location: India
Followed by:1 members
GMAT Score:540

by pardeep_10sharma » Sat May 22, 2010 7:41 am
Thanks for ur reply ...........good method..ton of thanks
Top
User avatar
GMAT Instructor
Posts: 613
Joined: Thu Mar 22, 2007 6:17 am
Location: madrid
Thanked: 171 times
Followed by:64 members
GMAT Score:790

by kevincanspain » Sat May 22, 2010 9:53 am
pardeep_10sharma wrote:A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > Suare root (2)
B. {Square root( 3) }/ 2 < y < Square root (2)
C. {Square root( 2) }/ 3 < y < {Square root( 3) }/ 2
D. {Square root( 3) }/ 4 < y < {Square root( 2) }/ 3
E. y < {Square root( 3) }/ 4

Ans is :- A ............Plz help

Also, the two legs measure x and y, so the area is xy/2

Since x < y, xy/2 < y^2/2

Thus y^2/2 > 1 and therefore y^2 > 2 i.e. y > sqrt(2)
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
Top
Senior | Next Rank: 100 Posts
Posts: 96
Joined: Fri Apr 23, 2010 1:14 am
Thanked: 1 times
Followed by:1 members

by quantskillsgmat » Sun May 23, 2010 2:45 am
z is hypotaneous and x and y are legs
so 1/2xy=1 so xy=2
since x<y, so xy/2<y^2/2 so y>root2
quantskillsgmat
wisdommart delhi
Top
Post new topic Post Reply
• Page 1 of 1