Last visit was: 09 Sep 2024, 22:07 It is currently 09 Sep 2024, 22:07
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A certain right triangle has sides of length x, y, and z, where x < y

SORT BY:
Date
Kudos
 1   2   
Tags:
Difficulty: 655-705 Level,   Geometry,   Inequalities,                  
Find Similar Topics 
Show Tags
Hide Tags
User avatar
tonebeeze
Manager
Manager
Joined: 19 Nov 2009
Status:Current MBA Student
Posts: 79
Own Kudos [?]: 2861 [704]
Given Kudos: 210
Concentration: Finance, General Management
Schools: Tuck '15 (A) CBS '15 (A) Wharton '15 (M) Booth '15 (A) Haas '15 (A) Stanford '15 (D)
GMAT 1: 720 Q49 V40
Send PM
A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   16 Jan 2011, 16:01
26
Kudos
676
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

60% (02:23) correct 40% (02:39) wrong based on 5233 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
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. \(y > \sqrt {2}\)

B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

E. \(y < \frac {\sqrt {3}}{4}\)
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95390
Own Kudos [?]: 657126 [292]
Given Kudos: 87212
Send PM
CAT Tests Forum Quiz Mode
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   16 Jan 2011, 16:12
160
Kudos
131
Bookmarks
Expert Reply
tonebeeze 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. \(y > \sqrt {2}\)

b. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

c. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

d. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

e. \(y < \frac {\sqrt {3}}{4}\)


The area of the triangle is \(\frac{xy}{2}=1\) (\(x<y<z\) means that hypotenuse is \(z\)) --> \(x=\frac{2}{y}\). As \(x<y\), then \(\frac{2}{y}<y\) --> \(2<y^2\) --> \(\sqrt{2}<y\).

Answer: A.

Also note that max value of \(y\) is not limited at all. For example \(y\) can be \(1,000,000\) and in this case \(\frac{xy}{2}=\frac{x*1,000,000}{2}=1\) --> \(x=\frac{2}{1,000,000}\).

Hope it helps.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15295
Own Kudos [?]: 67939 [40]
Given Kudos: 441
Location: Pune, India
Send PM
A certain right triangle has sides of length x, y, and z, wh [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   27 Apr 2016, 20:00
30
Kudos
10
Bookmarks
Expert Reply
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) \(y >\sqrt{2}\)

(B) \(\frac{\sqrt{3}}{2}<y<\sqrt{2}\)

(C) \(\frac{\sqrt{2}}{3}<y<\frac{\sqrt{3}}{2}\)

(D) \(\frac{\sqrt{3}}{4} < y <\frac{\sqrt{2}}{3}\)

(E) \(y<\frac{\sqrt{3}}{4}\)



You can think about it in terms of transition points too.

x < y< z so this means that x and y are the legs of the right triangle and z is the hypotenuse.
The area of the triangle will be (1/2)*xy = 1
xy = 2

Now, if x = y, then both x and y would be equal to \(\sqrt{2}\).
But y is greater than x, so y would be at least a slight bit greater than \(\sqrt{2}\) and x would be a slight bit less than \(\sqrt{2}\). In all options other than (A), y takes values less than 1.414.
Answer (A)
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 31253 [33]
Given Kudos: 799
Location: Canada
Send PM
A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   Updated on: 21 Jan 2021, 15:57
26
Kudos
7
Bookmarks
Expert Reply
Top Contributor
tonebeeze 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. \(y > \sqrt {2}\)

b. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

c. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

d. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

e. \(y < \frac {\sqrt {3}}{4}\)


Area of triangle \(= \frac{base \times height}{2}\)

There are infinitely many right triangles that have an area of 1.
So, one approach is to find a triangle that meets the given conditions, and then see what conclusions we can draw.

Here's one such right triangle:

Aside: There's no need to calculate the actual value of z (which is √5), since the question isn't asking us about the possible values of z.

This triangle meets the condition that its area is 1, and that x < y < z
With this particular triangle, y = 2

When we check the answer choices, only one option (answer choice A) allows for y to equal 2

Answer: A

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 11 Sep 2017, 13:54.
Last edited by BrentGMATPrepNow on 21 Jan 2021, 15:57, edited 3 times in total.
General Discussion
User avatar
rohansharma
Intern
Intern
Joined: 07 Feb 2011
Status:Focus is the Key
Posts: 7
Own Kudos [?]: 27 [1]
Given Kudos: 26
Concentration: Strategy, Technology
Schools: ISB
GMAT 1: 710 Q49 V38
GPA: 3.35
WE:Consulting (Telecommunications)
Send PM
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   06 Aug 2011, 04:41
1
Kudos
Bunuel wrote:
tonebeeze 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. \(y > \sqrt {2}\)

b. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

c. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

d. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

e. \(y < \frac {\sqrt {3}}{4}\)


The area of the triangle is \(\frac{xy}{2}=1\) (\(x<y<z\) means that hypotenuse is \(z\)) --> \(x=\frac{2}{y}\). As \(x<y\), then \(\frac{2}{y}<y\) --> \(2<y^2\) --> \(\sqrt{2}<y\).

Answer: A.

Also note that max value of \(y\) is not limited at all. For example \(y\) can be \(1,000,000\) and in this case \(\frac{xy}{2}=\frac{x*1,000,000}{2}=1\) --> \(x=\frac{2}{1,000,000}\).

Hope it helps.



Dear Bunuel,

While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95390
Own Kudos [?]: 657126 [1]
Given Kudos: 87212
Send PM
CAT Tests Forum Quiz Mode
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   09 Feb 2012, 04:42
1
Kudos
Expert Reply
rohansharma wrote:
While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?


We are just told that the triangle is right, not that it's a special kind like 30-60-90 or 45-45-90.
avatar
subhajeet
Manager
Manager
Joined: 12 Jun 2010
Status:MBA Aspirant
Posts: 78
Own Kudos [?]: 251 [4]
Given Kudos: 1
Location: India
Concentration: Finance, International Business
WE:Information Technology (Investment Banking)
Send PM
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   09 Feb 2012, 06:54
4
Kudos
OA is A
since this is a rt angled triangle so z is th hypotnuse
and given xy = 2
so as x decreased y increases. Now if x is 1 then y is 2, when x is 1/2 y is 4.
Only option A supports this result.
avatar
2flY
Intern
Intern
Joined: 31 Dec 2012
Posts: 4
Own Kudos [?]: 7 [1]
Given Kudos: 55
GMAT 1: 700 Q44 V42
Send PM
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   28 Feb 2013, 09:55
1
Bookmarks
Bunuel wrote:
\(x=\frac{2}{y}\). As \(x<y\), then \(\frac{2}{y}<y\)




Could you explain why that is?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95390
Own Kudos [?]: 657126 [4]
Given Kudos: 87212
Send PM
CAT Tests Forum Quiz Mode
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   28 Feb 2013, 10:01
4
Kudos
Expert Reply
2flY wrote:
Bunuel wrote:
\(x=\frac{2}{y}\). As \(x<y\), then \(\frac{2}{y}<y\)




Could you explain why that is?


Just substitute x with \(\frac{2}{y}\) in \(x<y\) to get \(\frac{2}{y}<y\).
User avatar
WoundedTiger
Director
Director
Joined: 25 Apr 2012
Posts: 527
Own Kudos [?]: 2345 [0]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Send PM
Reviews Badge
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   01 Mar 2013, 02:21
rohansharma wrote:
Bunuel wrote:
tonebeeze 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. \(y > \sqrt {2}\)

b. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

c. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

d. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

e. \(y < \frac {\sqrt {3}}{4}\)


The area of the triangle is \(\frac{xy}{2}=1\) (\(x<y<z\) means that hypotenuse is \(z\)) --> \(x=\frac{2}{y}\). As \(x<y\), then \(\frac{2}{y}<y\) --> \(2<y^2\) --> \(\sqrt{2}<y\).

Answer: A.

Also note that max value of \(y\) is not limited at all. For example \(y\) can be \(1,000,000\) and in this case \(\frac{xy}{2}=\frac{x*1,000,000}{2}=1\) --> \(x=\frac{2}{1,000,000}\).

Hope it helps.



Dear Bunuel,

While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?



Hi Bunuel,

The Q stem says that sides are x<y<z and it is a right angle triangle. So we can assume that it will be 30-60-90 triangle. Had it been 45-45-90 triangle then the 2 sides ie base and perpendicular would have been equal and therefore x=y and x,y<z

I guess it should be okay to assume that it is 30-60 -90 triangle.

Please confirm
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95390
Own Kudos [?]: 657126 [3]
Given Kudos: 87212
Send PM
CAT Tests Forum Quiz Mode
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   01 Mar 2013, 02:50
1
Kudos
2
Bookmarks
Expert Reply
mridulparashar1 wrote:
rohansharma wrote:
Bunuel wrote:
The area of the triangle is \(\frac{xy}{2}=1\) (\(x<y<z\) means that hypotenuse is \(z\)) --> \(x=\frac{2}{y}\). As \(x<y\), then \(\frac{2}{y}<y\) --> \(2<y^2\) --> \(\sqrt{2}<y\).

Answer: A.

Also note that max value of \(y\) is not limited at all. For example \(y\) can be \(1,000,000\) and in this case \(\frac{xy}{2}=\frac{x*1,000,000}{2}=1\) --> \(x=\frac{2}{1,000,000}\).

Hope it helps.



Dear Bunuel,

While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?



Hi Bunuel,

The Q stem says that sides are x<y<z and it is a right angle triangle. So we can assume that it will be 30-60-90 triangle. Had it been 45-45-90 triangle then the 2 sides ie base and perpendicular would have been equal and therefore x=y and x,y<z

I guess it should be okay to assume that it is 30-60 -90 triangle.

Please confirm


Yes, if it were 45-45-90, then we would have that x=y<z. BUT, knowing that it's not a 45-45-90 right triangle does NOT mean that it's necessarily 30-60-90 triangle: there are numerous other right triangles. For example, 10-80-90, 11-79-90, 25-65-90, ...

Hope it's clear.
avatar
B
Dienekes
Manager
Manager
Joined: 13 Feb 2011
Posts: 63
Own Kudos [?]: 184 [2]
Given Kudos: 3386
Send PM
GMAT ToolKit User
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   12 Feb 2016, 19:34
1
Kudos
1
Bookmarks
One other way that I noticed to solve this problem is to check the length of \(y\) when \(x=y\), i.e. 45,45,90. In that case \(x=y=\sqrt{2}\), however as \(y>x\), it'd always need to be \(>\sqrt{2}\).

HTH
User avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2353
Own Kudos [?]: 3662 [4]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Send PM
GMAT ToolKit User Reviews Badge
A certain right triangle has sides of length x, y, and z, wh [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   27 Apr 2016, 20:12
1
Kudos
3
Bookmarks
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) \(y >\sqrt{2}\)

(B) \(\frac{\sqrt{3}}{2}<y<\sqrt{2}\)

(C) \(\frac{\sqrt{2}}{3}<y<\frac{\sqrt{3}}{2}\)

(D) \(\frac{\sqrt{3}}{4} < y <\frac{\sqrt{2}}{3}\)

(E) \(y<\frac{\sqrt{3}}{4}\)



First step will be to breakdown the options into recognizable decimal representations (assuming \(\sqrt{2} \approx 1.4\), \(\sqrt{3} \approx 1.7\))

A) y>1.4
B) 0.8<y<1.4
C) 0.5<y<0.8
D) 0.4<y<0.5
E) y<0.4

We are given that x<y<z and that 0.5*x*y=1 --> x*y=2

Now from the relation xy=2 --> go back to the options and test for y=1. You get x=2 but we are given that x<y ---> y MUST be > \(\approx\)1.4 such that x < y

For any value of y < 1.4 , you will end up getting x>y (try with y=0.5 or 0.75 etc).

Only A satisfies this condition and is hence the correct answer.

Hope this helps.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15295
Own Kudos [?]: 67939 [6]
Given Kudos: 441
Location: Pune, India
Send PM
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   14 Dec 2017, 05:17
5
Kudos
Expert Reply
tonebeeze 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. \(y > \sqrt {2}\)

B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

E. \(y < \frac {\sqrt {3}}{4}\)



Since it is a right triangle, z is the greatest side and hence the hypotenuse.

So area of the triangle will be (1/2)*xy = 1
xy = 2

Note that x < y.
If x were equal to y, \(x = y = \sqrt{2}\)
Since x is less than y, \(y > \sqrt{2}\) and \(x < \sqrt{2}\)

Answer (A)
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 31253 [2]
Given Kudos: 799
Location: Canada
Send PM
A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   Updated on: 17 May 2021, 07:25
2
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) \(y >\sqrt{2}\)

(B) \(\frac{\sqrt{3}}{2}<y<\sqrt{2}\)

(C) \(\frac{\sqrt{2}}{3}<y<\frac{\sqrt{3}}{2}\)

(D) \(\frac{\sqrt{3}}{4} < y <\frac{\sqrt{2}}{3}\)

(E) \(y<\frac{\sqrt{3}}{4}\)


If x < y < z, then our RIGHT triangle looks something like this (where the hypotenuse is always the longest side)


When we scan the answer choices (ALWAYS scan the answer choices before performing any calculations!), I see that B, C, D and E all provide a MAXIMUM value of y.
This should be a bit of a surprise, because there's no limit to the length of each leg of the triangle.

GIVEN: The triangle has area 1
Area = (base)(height)/2
So, here's one possible triangle with area 1:

ASIDE: Area = (10)(0.2)/2 = 2/2 = 1 (voila!)

In this triangle, x = 0.2, y = 10 and z = some number greater than 10
Since it's possible for y to equal 10, we can eliminate answer choices B, C, D and E

Answer: A

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 12 Feb 2019, 12:09.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:25, edited 1 time in total.
User avatar
B
mimajit
Manager
Manager
Joined: 03 Aug 2017
Posts: 76
Own Kudos [?]: 26 [1]
Given Kudos: 85
Send PM
A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   26 Nov 2019, 04:22
1
Kudos
tonebeeze 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. \(y > \sqrt {2}\)

B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

E. \(y < \frac {\sqrt {3}}{4}\)


Since it is a right triangle, z is the greatest side and hence the hypotenuse.

So area of the triangle will be (1/2)*xy = 1
xy = 2

Note that x < y.
so for XY to be 2 either x=2 and Y=1 or Y =2 and X =1

we are already told x < y. so Y has to be 2.... and Root2 = 1.4 and since we now know y =2 option A
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5358
Own Kudos [?]: 4355 [0]
Given Kudos: 161
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   20 Apr 2020, 00:57
tonebeeze 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. \(y > \sqrt {2}\)

B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)

C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)

D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)

E. \(y < \frac {\sqrt {3}}{4}\)


Given: A certain right triangle has sides of length x, y, and z, where x < y < z.

Asked: If the area of this triangular region is 1, which of the following indicates all of the possible values of y?

Area of right triangle = xy/2 = 1
xy = 2
x = 2/y < y
\(y^2 >2\)
\(y > \sqrt{2}\)

IMO A
User avatar
S
rahulbhusan
Intern
Intern
Joined: 08 Jan 2020
Posts: 34
Own Kudos [?]: 16 [1]
Given Kudos: 0
Send PM
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   29 Aug 2020, 06:27
1
Kudos
Given, the area of this triangular region is 1 and x < y < z.
So, area of triangle= 1/2*x*y ( as it's a right angled triangle, so z must be the hypotenuse, and x and y can be either base or height)
=> 1/2*x*y=1
=> x*y=2
now, lets find the minimum value for y (or maximum value of x).
As, its a right angled triangle, the maximum value of x will be when its a isosceles right triangle i.e. 45:45:90 triangle.
=> x=y<z
so, x*y=2
=>x*x=2 (i.e minimum value of y)
=> x^2=2
=> x=√2
But, as we know that y>x,
so, y>√2. Option A
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 949
Own Kudos [?]: 239 [0]
Given Kudos: 432
Location: United States
Send PM
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   09 Nov 2020, 13:43
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?

We can approximate:
\(\sqrt{2} = 1.4\)
\(\sqrt{3} = 1.7\)

If the area of the triangular region = 1, this means \(\frac{xy}{2} = 1\)

A) \(y > 1.4\)

B) \(0.7 < y < 1.4\)

C) \(\frac{1.4}{3} < y < \frac{1.7}{2}\)

D) \(\frac{1.7}{4} < y < \frac{1.4}{3}\)

E) \(y < \frac{1.7}{4}\)

The only range that works is \(y > 1.4\). Answer is A.
avatar
B
anniaustin
Intern
Intern
Joined: 18 Dec 2019
Posts: 27
Own Kudos [?]: 8 [0]
Given Kudos: 16
Send PM
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink] A certain right triangle has sides of length x, y, and z, where x < y   09 Nov 2020, 14:10
\(xy=2\),
or, \(x=\frac{2}{y}\)
\(x<y\)
or, \(\frac{2}{y}<y\)
or, \(2<y^2\)
or, \(y>2\)

Answer: A
GMAT Club Bot
gmatclubot
Re: A certain right triangle has sides of length x, y, and z, where x < y [#permalink]
09 Nov 2020, 14:10
 1   2   
Moderator:
Bunuel
Math Expert
95390 posts