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If a square region has area n, what is the length of the dia

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If a square region has area n, what is the length of the dia [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) \(\sqrt{2n}\)
(B) \(\sqrt{n}\)
(C) \(2\sqrt{n}\)
(D) 2n
(E) 2n^2

Problem Solving
Question: 76
Category: Geometry Area; Pythagorean theorem
Page: 71
Difficulty: 600


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Re: If a square region has area n, what is the length of the dia [#permalink]

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SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) \(\sqrt{2n}\)
(B) \(\sqrt{n}\)
(C) \(2\sqrt{n}\)
(D) 2n
(E) 2n^2

The area of a square is \(\frac{diagonal^2}{2}\).

\(\frac{diagonal^2}{2}=n\) --> \(diagonal=\sqrt{2n}\).

Answer: A.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If a square region has area n, what is the length of the dia [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) \(\sqrt{2n}\)
(B) \(\sqrt{n}\)
(C) \(2\sqrt{n}\)
(D) 2n
(E) 2n^2


Area of square = n,
Hence each of the sides of the square are \(\sqrt{n}\)

Now the sides of any rectangular isosceles triangle have a ratio of 1:1:\(\sqrt{2}\).

Applying this ratio to a rectangular isosceles triangle whose equal sides are \(\sqrt{n}\), the ratio of the sides for this triangle becomes:
\(\sqrt{n}:\sqrt{n}:\sqrt{2}\sqrt{n}\)

Which is equivalent to
\(\sqrt{n} : \sqrt{n} : \sqrt{2n}\)

Answer: A
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Re: If a square region has area n, what is the length of the dia [#permalink]

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New post 05 Feb 2014, 07:19
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Ans A

Area of square=n=(side)^2
\sqrt{n}=side
(Diagonal)^2= (\sqrt{n})^2 + (\sqrt{n})^2
Diagonal=\sqrt{n+n}
=\sqrt{2n}
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Re: If a square region has area n, what is the length of the dia [#permalink]

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Hi All,

This question can be solved by TESTing VALUES.

We're told that a square has an AREA of N. We're asked for the length of the diagonal of that square.....

IF...
Side of the square = 3....
the area of the square = N = (3)(3) = 9....
the diagonal of the square = 3√2

Answer A: √(2N) = √(18) = 3√2 This IS a match.
Answer B: √N = √9 = 3 NOT a match.
Answer C: 2√N = 2√9 = 6 NOT a match.
Answer D: 2N = 18 NOT a match.
Answer E: 2N^2 = 162 NOT a match.

Final Answer:
[Reveal] Spoiler:
A


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Re: If a square region has area n, what is the length of the dia [#permalink]

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New post 20 Jan 2017, 10:33
Area = s^2
Area represented as n
n = s^2
each side s = \(\sqrt{n}\)
Diagonal of a square =\(s\sqrt{2}\)
Diagonal = \(\sqrt{n}\)\(\sqrt{2}\)
\(\sqrt{2n}\)
A
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Re: If a square region has area n, what is the length of the dia [#permalink]

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New post 21 Feb 2018, 00:35
Bunuel wrote:
SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) \(\sqrt{2n}\)
(B) \(\sqrt{n}\)
(C) \(2\sqrt{n}\)
(D) 2n
(E) 2n^2

The area of a square is \(\frac{diagonal^2}{2}\).

\(\frac{diagonal^2}{2}=n\) --> \(diagonal=\sqrt{2n}\).

Answer: A.



Hi Bunuel,

can you please explain one thing. Square has all sides of equal lenght. And if Diagonal divides square into two triangles.

How can such triangle be a RIGHT trangle ? It has two sides equal and two angles equal which is an Isosceles Triangle. Right?

Have an awesome day :)
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Re: If a square region has area n, what is the length of the dia [#permalink]

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New post 21 Feb 2018, 00:45
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dave13 wrote:
Bunuel wrote:
SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) \(\sqrt{2n}\)
(B) \(\sqrt{n}\)
(C) \(2\sqrt{n}\)
(D) 2n
(E) 2n^2

The area of a square is \(\frac{diagonal^2}{2}\).

\(\frac{diagonal^2}{2}=n\) --> \(diagonal=\sqrt{2n}\).

Answer: A.



Hi Bunuel,

can you please explain one thing. Square has all sides of equal lenght. And if Diagonal divides square into two triangles.

How can such triangle be a RIGHT trangle ? It has two sides equal and two angles equal which is an Isosceles Triangle. Right?

Have an awesome day :)


Don't we have a right angle there? We'll get two isosceles right triangles. You could draw a square and divide it into two triangles with a diagonal, should be easy to check.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If a square region has area n, what is the length of the dia [#permalink]

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New post 21 Feb 2018, 19:43
dave13 wrote:
Bunuel wrote:
SOLUTION

If a square region has area n, what is the length of the diagonal of the square in terms of n ?

(A) \(\sqrt{2n}\)
(B) \(\sqrt{n}\)
(C) \(2\sqrt{n}\)
(D) 2n
(E) 2n^2

The area of a square is \(\frac{diagonal^2}{2}\).

\(\frac{diagonal^2}{2}=n\) --> \(diagonal=\sqrt{2n}\).

Answer: A.



Hi Bunuel,

can you please explain one thing. Square has all sides of equal lenght. And if Diagonal divides square into two triangles.

How can such triangle be a RIGHT trangle ? It has two sides equal and two angles equal which is an Isosceles Triangle. Right?

Have an awesome day :)


Hi dave13,

When you cut a square in half (from corner to opposite corner), you always end up with two 45/45/90 right triangles (and yes, they are Isosceles triangles). With tougher Geometry questions on the GMAT, you should look for common shapes (such as right triangles) inside of larger (or more complex) shapes. Sometimes the 'key' to solving those types of prompts is to redraw a picture by 'breaking' it into pieces and then using the appropriate Geometry formulas to complete the calculations.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If a square region has area n, what is the length of the dia   [#permalink] 21 Feb 2018, 19:43
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