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

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Re: If a square region has area n, what is the length of the diagonal of [#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}
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Re: If a square region has area n, what is the length of the diagonal of [#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.

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

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

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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 diagonal of [#permalink]
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 = n = a^2 ; where a is the side of the square

$$a = \sqrt{n}$$

Diagonal = $$a\sqrt{2} = \sqrt{n}\sqrt{2} = \sqrt{2n}$$

IMO A
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Re: If a square region has area n, what is the length of the diagonal of [#permalink]
Bunuel wrote:
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

$$A = \frac{d^2}{2}$$

Or, $$n = \frac{d^2}{2}$$

Or, $$2n = d^2$$

So, $$d = \sqrt{2n}$$, Answer must be (A)
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Re: If a square region has area n, what is the length of the diagonal of [#permalink]
Bunuel wrote:
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

Hi Bunuel,

isn't the formula "a(square root)2"? can you give an example of a square that would make sense? if the side is 4 for example, the diagonal would be 5.666, but according to the formula it would be 2.8...?
thx
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Re: If a square region has area n, what is the length of the diagonal of [#permalink]
jaydavido wrote:
Bunuel wrote:
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

Hi Bunuel,

isn't the formula "a(square root)2"? can you give an example of a square that would make sense? if the side is 4 for example, the diagonal would be 5.666, but according to the formula it would be 2.8...?
thx

I'm not sure I understand your question...

The area of a square can be calculated using the formula side^2 or by using the formula (diagonal^2)/2. If the length of a side of a square is 4, then its diagonal measures 4√2, and its area = side^2 = (diagonal^2)/2 = 16.
Re: If a square region has area n, what is the length of the diagonal of [#permalink]
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