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Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Re: Is the length of a side of equilateral triangle E less than [#permalink]

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04 Mar 2014, 17:35

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

Re: Is the length of a side of equilateral triangle E less than [#permalink]

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04 Mar 2014, 20:25

bparrish89 wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

The second statement states the ratio as 2√3 : 3√2 &, the calculated ratio is x√3/2 : y√2. Now if these two ratios are same, we just need to simplify the equation, which gives the ratio of x:y to 4:3.

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

Re: Is the length of a side of equilateral triangle E less than [#permalink]

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05 Mar 2014, 08:07

bparrish89 wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

If equilateral triangle has height 2square root 3.. that means its all sides will be 4.. and if diagonal of square is 3 square root2 that means square has all sides 3.

we got No ! equilateral triangle length is greater than square's length
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Re: Is the length of a side of equilateral triangle E less than [#permalink]

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05 Mar 2014, 15:05

Bunuel wrote:

bparrish89 wrote:

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{x\frac{\sqrt{3}}{2}}{y\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

Bunuel - Could you explain how you simplified the ratio in statement #2 to get to x/y = 4/3?

Re: Is the length of a side of equilateral triangle E less than [#permalink]

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05 Mar 2014, 17:22

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

In 2 above, can you tell me how you got y√2?

y is the length of a side of square F. Now, the diagonal of a square is the hypotenuse of a right isosceles triangle made by the sides:

Attachment:

square.jpg [ 10.18 KiB | Viewed 3380 times ]

Therefore by Pythagorean theorem \(y^2+y^2=diagonal^2\) --> \(2y^2=diagonal^2\) --> \(diagonal=y\sqrt{2}\).

Re: Is the length of a side of equilateral triangle E less than [#permalink]

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17 Mar 2015, 19:12

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Could you please explain how did you get the calculated height of the equilateral triangle in statement 2? Thanks

hi millopezle Is the length of a side of equilateral triangle E less than the length of a side of square F?

(1) The perimeter of E and the perimeter of F are equal. (2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2

since you are asking specific question about statement 2.. it is giving us the ratio of height of triangle E to the diagonal of square F as 2√3 : 3√2... since its a ratio ,we can multiply both by x, although we dont require that because final answer is also a ratio... from height of triangle , we can get its side by formula.. h=side1*√3/2... from diagonal of square we can get side by formula... diagonal=√2*side2 what you require is side1/side2= 2h/√3*dia/√2=2/√6*h/dia=2/√6*2√3/3√2=2/3... so we have the ratio as 2/3.. so we can say side of square >side of tri... sufficient
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Re: Is the length of a side of equilateral triangle E less than [#permalink]

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20 May 2015, 14:02

Bunuel wrote:

Is the length of a side of equilateral triangle E less than the length of a side of square F?

Let x be the length of a side of equilateral triangle E and y be the length of a side of square F. Question: is x>y?

(1) The perimeter of E and the perimeter of F are equal --> 3x=4y --> x/y=4/3 --> x>y. Sufficient.

(2) The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2 --> the height of triangle E is \(x\frac{\sqrt{3}}{2}\) and the diagonal of square F is \(y\sqrt{2}\) --> ratio: \(\frac{(x\frac{\sqrt{3}}{2})}{(y\sqrt{2})}=\frac{2\sqrt{3}}{3\sqrt{2}}\) --> x/y=4/3 --> x>y. Sufficient.

Answer: D.

I have a Question, why do we assume that sides of these figures (triangle and square) are integers? If its a non-integer then the entire answer changes to E.

You bring up a fair point - we don't have to assume that the side lengths are integers, but it makes dealing with the 'logic' behind this question easier. As it stands, using non-integers will NOT change the answer to the question, but certain DS questions will require that you consider non-integer values, so it's a good idea to keep them in mind.

Re: Is the length of a side of equilateral triangle E less than [#permalink]

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20 May 2015, 23:36

EMPOWERgmatRichC wrote:

Hi earnit,

You bring up a fair point - we don't have to assume that the side lengths are integers, but it makes dealing with the 'logic' behind this question easier. As it stands, using non-integers will NOT change the answer to the question, but certain DS questions will require that you consider non-integer values, so it's a good idea to keep them in mind.

GMAT assassins aren't born, they're made, Rich

Thank you. I accidentally also missed the fact that changing the values to non-integer will not affect the ratio and the answer.

gmatclubot

Re: Is the length of a side of equilateral triangle E less than
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20 May 2015, 23:36

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