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

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Bunuel

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

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 \(\frac{diagonal^2}{2}\).

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

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

05 Feb 2014, 05:03

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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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AKG1593

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

05 Feb 2014, 08:19

Kudos

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]

21 May 2015, 20:30

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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:

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

20 Jan 2017, 11:33

Kudos

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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

dave13

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

21 Feb 2018, 01:35

Bunuel wrote:

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

Bunuel

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

21 Feb 2018, 01:45

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dave13 wrote:

Bunuel wrote:

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]

21 Feb 2018, 20:43

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dave13 wrote:

Bunuel wrote:

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]

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 \(\sqrt{n}\) = \(\sqrt{2}\sqrt{n}\) = \(\sqrt{2n}\)

Answer A

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]

29 Sep 2018, 10:33

Bunuel wrote:

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

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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 \(\sqrt{n} * \sqrt{2} = \sqrt{2n}\)

Answer choice A

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

21 Jul 2020, 10:44

Bunuel wrote:

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

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]

09 Oct 2021, 06:25

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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jaydavido

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Joined: 13 Dec 2022

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

23 Mar 2023, 04:44

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

Bunuel

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

23 Mar 2023, 05:08

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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

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.
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