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Math Expert V
Joined: 02 Sep 2009
Posts: 55150
A square has a diagonal of length x, what is the area of the square in  [#permalink]

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Difficulty:   15% (low)

Question Stats: 87% (00:51) correct 13% (01:08) wrong based on 53 sessions

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A square has a diagonal of length x, what is the area of the square in terms of x?

A. 4x^2
B. 2x^2
C. x^2
D. x^2/2
E. x^2/4

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Director  G
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Re: A square has a diagonal of length x, what is the area of the square in  [#permalink]

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Bunuel wrote:
A square has a diagonal of length x, what is the area of the square in terms of x?

A. 4x^2
B. 2x^2
C. x^2
D. x^2/2
E. x^2/4

if diagonal = x
side = x/root 2
area = side ^2 = x^2/2
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1005
WE: Supply Chain Management (Energy and Utilities)
Re: A square has a diagonal of length x, what is the area of the square in  [#permalink]

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1
Bunuel wrote:
A square has a diagonal of length x, what is the area of the square in terms of x?

A. 4x^2
B. 2x^2
C. x^2
D. x^2/2
E. x^2/4

Given , Length of diagonal=x
We know length of diagonal of square=$$\sqrt{2}*length of side$$
So, length of side=$$x/\sqrt{2}$$

Area of square=$$(x/\sqrt{2})^2=\frac{x^2}{2}$$

Ans. (D)
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PKN

Rise above the storm, you will find the sunshine
Intern  B
Joined: 09 Sep 2018
Posts: 16
Re: A square has a diagonal of length x, what is the area of the square in  [#permalink]

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wrong tag. this is not 600-700. This is 300-500.

Don't fool us please Director  G
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: A square has a diagonal of length x, what is the area of the square in  [#permalink]

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45:45:90 triangle is formed when we have a diagonal of a square

Since the question stem has x as a variable we let the values from the 45:45:90 be y

y:y: y sqrt 2

We know the diagonal is x so x = y sqrt 2

Now y = x/ sqrt 2

Area = y^2 = (x/sqrt 2)^2 = x^2/2

Answer choice D

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VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1005
WE: Supply Chain Management (Energy and Utilities)
Re: A square has a diagonal of length x, what is the area of the square in  [#permalink]

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martinod20 wrote:
wrong tag. this is not 600-700. This is 300-500.

Don't fool us please Hi martinod20,

It may be noted that level of the question is determined based on the results of timer attempts by the GC users. You may notice that 72% is the optimum correct response,though the question seems easy to you.

Hope it helps.
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Regards,

PKN

Rise above the storm, you will find the sunshine
Director  V
Joined: 12 Feb 2015
Posts: 837
Re: A square has a diagonal of length x, what is the area of the square in  [#permalink]

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martinod20 wrote:
wrong tag. this is not 600-700. This is 300-500.

Don't fool us please I think it seems to be sub 600 level question. Its easy, straightforward but it does require you to recall some concepts and use them. I feel its ok!
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Manish "Only I can change my life. No one can do it for me" Re: A square has a diagonal of length x, what is the area of the square in   [#permalink] 29 Sep 2018, 11:00
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# A square has a diagonal of length x, what is the area of the square in

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