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If the area of square A is three times the area of square B

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If the area of square A is three times the area of square B  [#permalink]

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New post Updated on: 30 Jan 2014, 22:44
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If the area of square A is three times the area of square B, what is the ratio of the diagonal of square A to that of square B?

A. \(\frac{1}{\sqrt{3}}\)

B. \(\frac{1}{\sqrt[3]{3}}\)

C. \(\sqrt[3]{3}\)

D. \(\sqrt{3}\)

E. 3

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Originally posted by slingfox on 25 Oct 2009, 22:22.
Last edited by Bunuel on 30 Jan 2014, 22:44, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: Ratio of Triangle Measurements  [#permalink]

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New post 25 Oct 2009, 23:32
1
slingfox wrote:
If the area of square Q is three times the area of square P, what is the ratio of the diagonal of square Q to that of square?

A. 1/Sqrt(3)
B. 1/Third Root(3)
C. Third Root(3)
D. Sqrt(3)
E. 3


Area of small square-P = s^2
Side of small square-P = s
Diagonal of a small square-P = s (sqrt2)

Area of large square-Q = 3s^2
Side of large square-Q = s {sqrt(3)}
Diagonal of a large square-Q = s (sqrt6)

Diagonal of a large square-Q / Diagonal of a small square-P = s (sqrt6) / s (sqrt2) = sqrt3
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Re: Ratio of Triangle Measurements  [#permalink]

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New post 26 Oct 2009, 06:07
Area Q = 3a^2

Area P = 3b^2.

3a^2 = 3b^2.

a = sqrt(3)*b.

diagonal of Q = sqrt(2) * a

diagonal of P = sqrt(2) * b.

Ratio of Q/P = a/b = sqrt(3) * b/b = sqrt(3).

I will go with option D
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Re: Ratio of Triangle Measurements  [#permalink]

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New post 26 Oct 2009, 09:29
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I wouldn't waste time calculating the ratio of the diagonals, calculating the ratio of the sides would suffice as it equals the ratio of the diagonals.
i.e. a/b = sqrt2*a/sqrt2*b.
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Re: Ratio of Triangle Measurements  [#permalink]

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New post 26 Oct 2009, 09:35
true, we just need to calculate ratio of sides ps to qs (as the ratio of diagonals is same as ratio of sides because diagonal is always \(sqrt2\) times side)

given that \(p^2/q^2=3
==> p/q=sqrt3\)
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Re: Ratio of Triangle Measurements  [#permalink]

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New post 30 Oct 2009, 21:33
sqr(e1)/sqr(e2) = 3/1

e1/e2 = sqrt(3)

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Re: Ratio of Triangle Measurements  [#permalink]

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New post 30 Oct 2009, 22:02
nice approach atish. diagonal is \(sqrt(2)\) x side
In test conditions, these things never comes to mind :(
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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 30 Jan 2014, 22:49
1
slingfox wrote:
If the area of square A is three times the area of square B, what is the ratio of the diagonal of square A to that of square B?

A. \(\frac{1}{\sqrt{3}}\)

B. \(\frac{1}{\sqrt[3]{3}}\)

C. \(\sqrt[3]{3}\)

D. \(\sqrt{3}\)

E. 3


The area of a square is \(\frac{diagonal^2}{2}\).

Hence we are given that \(\frac{D^2}{2}=3*\frac{d^2}{2}\) --> \(\frac{D}{d}=\sqrt{3}\).

Answer: D.
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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 30 Jan 2014, 23:19
slingfox wrote:
If the area of square A is three times the area of square B, what is the ratio of the diagonal of square A to that of square B?

A. \(\frac{1}{\sqrt{3}}\)

B. \(\frac{1}{\sqrt[3]{3}}\)

C. \(\sqrt[3]{3}\)

D. \(\sqrt{3}\)

E. 3


Let us say that area of A is 12 and area of B is 4.
Side of A = 2(3)^1/2
Side of B = 2
Diagonal of A/Diagonal of B = (Side of A)/(Side of B) = (3^1/2)/1

Answer is D
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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 09 Mar 2014, 22:01
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Say area of Square B = 1 (Each side = 1), then
Area of Square A = 3 (Each side = \(\sqrt{3}\))

Diagonal of Square A = \(\sqrt{6}\)

Diagonal of Square B = \(\sqrt{2}\)

Ratio = \(\sqrt{3}\)

Answer =D
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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 20 May 2014, 12:18
Am I going crazy or is there something wrong with this GMATClub CAT question? I don't think the correct answer is listed.

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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 20 May 2014, 12:42
Kenny537 wrote:
Am I going crazy or is there something wrong with this GMATClub CAT question? I don't think the correct answer is listed.

Image

Just realized the answer is meant to be (1/sqrt of 3) rather than (1/3.5). Now it makes sense. Hard to tell.
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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 21 May 2014, 00:59
Dear Kenny537,
Problem at gmat club is asking for the ratio of the diagonal of square A to that of square B while in the image attached by you, the ratio of the diagonal of square B to that of square A is being asked.

Accordingly, answer is right in both the questions because both are asking different ratios.
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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 21 May 2014, 07:23
kundankshrivastava wrote:
Dear Kenny537,
Problem at gmat club is asking for the ratio of the diagonal of square A to that of square B while in the image attached by you, the ratio of the diagonal of square B to that of square A is being asked.

Accordingly, answer is right in both the questions because both are asking different ratios.


I am aware that it is a different question. I just didn't feel like creating a thread for the question and thought this was a similar enough question.
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Re: If the area of square A is three times the area of square B  [#permalink]

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New post 20 Feb 2016, 04:39
A square is a rhombus. The area of a rhombus is 1/2 * d1 * d2. For a square, d1 = d2 (=d). Thus area = \(1/2 * d^2\)
If area is 3 times the other, the diagonal should be \sqrt{3} times the other.
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Re: If the area of square A is three times the area of square B  [#permalink]

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Re: If the area of square A is three times the area of square B &nbs [#permalink] 22 Sep 2018, 19:41
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