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Twice the length of the diagonal of the same rectangle
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26 Oct 2022, 01:12
26 Oct 2022, 01:12
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Question Stats:
55% (01:08) correct
44% (01:00) wrong based on 29 sessions
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Quantity A |
Quantity B |
The perimeter of a rectangle |
Twice the length of the diagonal of the same rectangle |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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GRE Math Essentials (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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Joined: 25 May 2022
Posts: 25
Given Kudos: 1
Twice the length of the diagonal of the same rectangle
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26 Oct 2022, 21:38
26 Oct 2022, 21:38
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Let's say the length is L and the width is W.
So the perimeter = 2(L + W)
And the double of the diagonal = \(2 × \sqrt{L^2 + W^2}\)
So we are comparing L + W and \(\sqrt{L^2 + W^2}\)
We can visualize a right-angle triangle here where \(\sqrt{L^2 + W^2}\) is the diagonal (one side) and L + W is the sum of the other two sides.
The answer is A.
So the perimeter = 2(L + W)
And the double of the diagonal = \(2 × \sqrt{L^2 + W^2}\)
So we are comparing L + W and \(\sqrt{L^2 + W^2}\)
We can visualize a right-angle triangle here where \(\sqrt{L^2 + W^2}\) is the diagonal (one side) and L + W is the sum of the other two sides.
- Hence L + W must be greater.
The answer is A.
Re: Twice the length of the diagonal of the same rectangle
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19 Sep 2024, 01:14
19 Sep 2024, 01:14
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Thanks to another GRE Prep 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).
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