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

Question

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

BrentGMATPrepNow · Accepted Answer

Here's what we're dealing with:
 https://i.imgur.com/DUh2Pma.png

We're dealing with a  right triangle 
So, we can apply the Pythagorean theorem to write:   k  ² +   k  ² = (  2√x  )²
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.

Answer: E

Cheers,
Brent

Kinshook · Answer

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

Nipunh1991 · Answer

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

Archit3110 · Answer

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

Avysar · Answer

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

ScottTargetTestPrep · Answer

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 = 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.

Answer: E

perfectreview · Answer

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

Batman117 · Answer

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

EgmatQuantExpert · Answer

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 .

Correct Answer: Option E

CrackverbalGMAT · Answer

Solution: Area of a square with diagonal length of d= d^2/2 d = 2√x =>Area = (2√x)^2/2 =2x (option e) Hope this helps

Devmitra Sen (GMAT Quant Expert)

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=q_-3JA-lW08

bumpbot · Answer

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

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

Prep Toolkit

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