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# The width, length, and diagonal of a rectangle could

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GRE Instructor
Joined: 10 Apr 2015
Posts: 2022
Followers: 62

Kudos [?]: 1841 [1] , given: 9

The width, length, and diagonal of a rectangle could [#permalink]  10 Jan 2019, 06:56
1
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Question Stats:

100% (01:46) correct 0% (00:00) wrong based on 3 sessions
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
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Director
Joined: 07 Jan 2018
Posts: 648
Followers: 7

Kudos [?]: 606 [0], given: 88

Re: The width, length, and diagonal of a rectangle could [#permalink]  10 Jan 2019, 07:08
Width, length and Diagonal of a rectangle should satisfy the Pythagoras theorem with diagonal as the largest side. Only option I satisfies the theorem.

$$2^2 + 3^2 = (\sqrt{13}$$)$$^2$$
GRE Instructor
Joined: 10 Apr 2015
Posts: 2022
Followers: 62

Kudos [?]: 1841 [1] , given: 9

Re: The width, length, and diagonal of a rectangle could [#permalink]  11 Jan 2019, 09:44
1
KUDOS
Expert's post
GreenlightTestPrep 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
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: The width, length, and diagonal of a rectangle could   [#permalink] 11 Jan 2019, 09:44
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