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

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Question Stats: 83% (00:52) correct 17% (01:05) wrong based on 851 sessions

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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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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Math Expert V
Joined: 02 Sep 2009
Posts: 59675
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 $$\frac{diagonal^2}{2}$$.

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

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Intern  Joined: 26 Feb 2012
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GMAT 3: 640 Q49 V29 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
$$\sqrt{n} : \sqrt{n} : \sqrt{2n}$$

##### General Discussion
Manager  Joined: 20 Dec 2013
Posts: 222
Location: India
Re: If a square region has area n, what is the length of the dia  [#permalink]

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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}
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 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.

GMAT assassins aren't born, they're made,
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Re: If a square region has area n, what is the length of the dia  [#permalink]

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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
VP  D
Joined: 09 Mar 2016
Posts: 1229
Re: If a square region has area n, what is the length of the dia  [#permalink]

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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 $$\frac{diagonal^2}{2}$$.

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

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 Math Expert V
Joined: 02 Sep 2009
Posts: 59675
Re: If a square region has area n, what is the length of the dia  [#permalink]

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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 $$\frac{diagonal^2}{2}$$.

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

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.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a square region has area n, what is the length of the dia  [#permalink]

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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 $$\frac{diagonal^2}{2}$$.

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

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

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let side of square is $$x$$
so, $$area=x^2$$
$$x^2=n$$
$$x=\sqrt{n}$$
As the diagonal length of a square with side length $$x$$ is = $$\sqrt{2}x$$
so, diagonal length of square with side length $$\sqrt{n}$$ = $$\sqrt{2}\sqrt{n}$$ = $$\sqrt{2n}$$

Alternately you can use pathagoras theorem to find diagonal length of square with side length $$\sqrt{n}$$
Director  G
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
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

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Area of square = x^2

Since we are given the area = n then the side equals $$\sqrt{n}$$

A diagonal in a square creates two 45:45:90 triangles.

45:45:90
x:x:x$$\sqrt{2}$$
since the side equals $$\sqrt{n}$$ then the diagonal would be $$\sqrt{n} * \sqrt{2} = \sqrt{2n}$$

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

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_________________ Re: If a square region has area n, what is the length of the dia   [#permalink] 25 Oct 2019, 07:32
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