Last visit was: 23 Jun 2024, 23:35 It is currently 23 Jun 2024, 23:35
Toolkit
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

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.

# The width, length, and diagonal of a rectangle could be represented by

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93964
Own Kudos [?]: 634410 [3]
Given Kudos: 82420
Verbal Forum Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2095
Own Kudos [?]: 8944 [0]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Manager
Joined: 07 May 2015
Posts: 159
Own Kudos [?]: 73 [1]
Given Kudos: 21
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6806
Own Kudos [?]: 30623 [1]
Given Kudos: 799
Re: The width, length, and diagonal of a rectangle could be represented by [#permalink]
1
Kudos
Bunuel wrote:
The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, $$\sqrt{13}$$
II. $$\sqrt{10}$$, 4, 6
III. 3, 10, 11

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

NOTE: The width, length, and diagonal create a RIGHT TRIANGLE, with the diagonal as the hypotenuse.
For these to be valid lengths, the Pythagorean Theorem must apply.
That is, it MUST be the case that width² + length² = diagonal²

Let's check the 3 sets of values BEGINNING WITH III

III. Does 3² + 10² = 11²? NO.
This means that 3, 10, 11 CANNOT represent the width, length, and diagonal of a rectangle.
This means we can ELIMINATE C, D and E

II. Does (√10)² + 4² = 6²? NO.
This means that √10, 4, 6 CANNOT represent the width, length, and diagonal of a rectangle.
This means we can ELIMINATE B

Cheers,
Brent
Manager
Joined: 14 Jun 2015
Posts: 80
Own Kudos [?]: 35 [0]
Given Kudos: 33
Location: India
GMAT 1: 680 Q46 V37
GMAT 2: 750 Q50 V40
GPA: 3.5
WE:Information Technology (Telecommunications)
Re: The width, length, and diagonal of a rectangle could be represented by [#permalink]
The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, 13‾‾‾√
II. 10‾‾‾√, 4, 6
III. 3, 10, 11

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

The Three dimensions of a rectangle in the given order represents the two side and the hypotenuse of a right angle trianlge.
Only set that obeys pythogerous theorem is I.
So Ans: A
Non-Human User
Joined: 09 Sep 2013
Posts: 33685
Own Kudos [?]: 841 [0]
Given Kudos: 0
Re: The width, length, and diagonal of a rectangle could be represented by [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: The width, length, and diagonal of a rectangle could be represented by [#permalink]
Moderator:
Math Expert
93964 posts