GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 15 Jul 2020, 02:45 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If the length of a diagonal of a square is 2x^(1/2), what is the area

Author Message
TAGS:

### Hide Tags

Manager  G
Joined: 03 Jun 2019
Posts: 79
If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

1
3 00:00

Difficulty:   5% (low)

Question Stats: 80% (01:12) correct 20% (01:16) wrong based on 214 sessions

### HideShow timer Statistics

If the length of a diagonal of a square is $$2\sqrt{x}$$, what is the area of the square in terms of x ?

A. $$\sqrt{x}$$

B. $$\sqrt{2x}$$

C. $$2\sqrt{x}$$

D. x

E. 2x

PS60231.02
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4961
GMAT 1: 770 Q49 V46
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

4
Top Contributor
parkhydel wrote:
If the length of a diagonal of a square is $$2\sqrt{x}$$, what is the area of the square in terms of x ?

A. $$\sqrt{x}$$

B. $$\sqrt{2x}$$

C. $$2\sqrt{x}$$

D. x

E. 2x

PS60231.02

Here's what we're dealing with: We're dealing with a right triangle
So, we can apply the Pythagorean theorem to write: k² + k² = (2√x
Simplify to get: 2k² = 4x
Divide both sides by 2 to get: k² = 2x

Since k = length of one side of the square, it follows that k² = the area of the square
Since k² = 2x, we can conclude that 2x = the area of the square.

Cheers,
Brent
_________________
##### General Discussion
CEO  V
Joined: 03 Jun 2019
Posts: 3258
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

1
parkhydel wrote:
If the length of a diagonal of a square is $$2\sqrt{x}$$, what is the area of the square in terms of x ?

A. $$\sqrt{x}$$

B. $$\sqrt{2x}$$

C. $$2\sqrt{x}$$

D. x

E. 2x

PS60231.02

Asked: If the length of a diagonal of a square is $$2\sqrt{x}$$, what is the area of the square in terms of x ?

Side of a square = $$Length of diagonal / \sqrt{2} =2\sqrt{x}/\sqrt{2} = \sqrt{2x}$$

Area of a square $$= (side)^2 = (\sqrt{2})^2 = 2x$$

IMO E
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Intern  B
Joined: 04 Jan 2016
Posts: 30
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

parkhydel wrote:
If the length of a diagonal of a square is $$2\sqrt{x}$$, what is the area of the square in terms of x ?

A. $$\sqrt{x}$$

B. $$\sqrt{2x}$$

C. $$2\sqrt{x}$$

D. x

E. 2x

PS60231.02

Well, if we know the relation between the diagonal and the side of a square. The problem becomes fairly simple.

Let us assume that the side of the square is 's'. The relation between the side of a square and its diagonal (d) is 'd= s $$\sqrt{2}$$

Hence,

s $$\sqrt{2}$$= 2 $$\sqrt{x}$$
(These two are equal since we are talking about the length of the same diagonal)

s = $$2 \sqrt{x}$$ / $$\sqrt{2}$$

Squaring both the sides (since area of a square is ($$S^2$$)

$$S^2$$ = $$\frac{4x}{2}$$

$$S^2$$ = 2x (Area of Square)

Hope this helps a little
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 6450
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

given that digonal of square = 2√x
we know that digonal of square = √2 * side of square
so from given info ; side of square = 2√x/2 ; √2x
area of square ( √2x) ^2 ; 2x
OPTION E

parkhydel wrote:
If the length of a diagonal of a square is $$2\sqrt{x}$$, what is the area of the square in terms of x ?

A. $$\sqrt{x}$$

B. $$\sqrt{2x}$$

C. $$2\sqrt{x}$$

D. x

E. 2x

PS60231.02
Intern  B
Joined: 24 Apr 2020
Posts: 41
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

Since it's a square we get an isoceles right triangle with the diagonal and the sides will be in the ratio
1:1:√2
?:?:2√x
So side of the square is2√x/√2
Square this for Area 4x/2=2x
Hence E

Posted from my mobile device
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11121
Location: United States (CA)
If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

1
parkhydel wrote:
If the length of a diagonal of a square is $$2\sqrt{x}$$, what is the area of the square in terms of x ?

A. $$\sqrt{x}$$

B. $$\sqrt{2x}$$

C. $$2\sqrt{x}$$

D. x

E. 2x

PS60231.02

Solution:

For a square, diagonal = side√2, so we have:

2√x= side√2

2√(x/2) = side

Thus, the area of the square is [2√(x/2)]^2 = 4(x/2) = 2x.

Alternate Solution:

The area of a square with diagonal length of d is A = d^2/2. Thus, the area of the square in question is (2√x)^2 / 2 = (4x)/2 = 2x.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

214 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern  B
Joined: 30 May 2020
Posts: 19
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

1
The area of a square when diagonal is give = $$\frac{1}{2}$$$$d^{2}$$

So the area now will be $$\frac{1}{2}*(2\sqrt{x})^{2}$$

= $$\frac{1}{2}$$ * 4x

= 2x
_________________
Founder
Perfect Review
http://www.perfectreview.co.in
Manager  B
Joined: 19 Jan 2019
Posts: 51
Location: India
Concentration: Operations, Strategy
GPA: 3.3
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

2 ways to approach this que.
1.with direct formula
Area = 1/2 (diagonal)^2

2.as pee info it is square and diagonal will cut right angle to 45:45.
So using 45:45:90 we can find side of square
Area= side^2

Posted from my mobile device
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3410
Re: If the length of a diagonal of a square is 2x^(1/2), what is the area  [#permalink]

### Show Tags

Solution

Given
• Length of a diagonal of a square = $$2 \sqrt{(x)}$$.

To Find
• Area of square in terms of x.

Approach and Working out
Let’s say that the square has all of its sides = a units. Area of the square will be $$a^2$$.
• Diagonal of the square can be found out using Pythagoras theorem since all the angles of the square are of 90 degrees each.
o Therefore $$a^2 + a^2 = diagonal ^2$$
o Therefore $$diagonal = \sqrt{(2a^2)}$$
.
Now, diagonal of the square $$= 2\sqrt{(x)} = \sqrt{(2a^2)}$$.
• Finding the side of the square (a) in terms of ‘x’: $$2a^2 = 4x$$.
o $$a^2 = 2x$$. Therefore $$a = \sqrt{(2x)}$$.

Area of a square $$= a^2 = (\sqrt{(2x)})^2 = 2x$$.

_________________ Re: If the length of a diagonal of a square is 2x^(1/2), what is the area   [#permalink] 31 May 2020, 07:08

# If the length of a diagonal of a square is 2x^(1/2), what is the area  