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

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

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05 Feb 2014, 02:19
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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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Re: If a square region has area n, what is the length of the dia  [#permalink]

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05 Feb 2014, 02:20
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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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Re: If a square region has area n, what is the length of the dia  [#permalink]

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05 Feb 2014, 05:03
3
4
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
$$\sqrt{n} : \sqrt{n} : \sqrt{2n}$$

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

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05 Feb 2014, 08:19
1
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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21 May 2015, 20:30
1
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.

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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!***** Manager Joined: 25 Mar 2013 Posts: 238 Location: United States Concentration: Entrepreneurship, Marketing GPA: 3.5 Re: If a square region has area n, what is the length of the dia [#permalink] ### Show Tags 20 Jan 2017, 11:33 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 _________________ I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you VP Joined: 09 Mar 2016 Posts: 1279 Re: If a square region has area n, what is the length of the dia [#permalink] ### Show Tags 21 Feb 2018, 01:35 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 Math Expert Joined: 02 Sep 2009 Posts: 53831 Re: If a square region has area n, what is the length of the dia [#permalink] ### Show Tags 21 Feb 2018, 01:45 1 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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13791 Location: United States (CA) 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] ### Show Tags 21 Feb 2018, 20:43 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 Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If a square region has area n, what is the length of the dia  [#permalink]

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10 Sep 2018, 09:35
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 $$\sqrt{n}$$
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Re: If a square region has area n, what is the length of the dia  [#permalink]

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29 Sep 2018, 10:33
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:
1. Please provide your solutions to the questions;
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 $$\sqrt{n} * \sqrt{2} = \sqrt{2n}$$

Re: If a square region has area n, what is the length of the dia   [#permalink] 29 Sep 2018, 10:33
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# If a square region has area n, what is the length of the dia

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