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Re: Is the length of a side of equilateral triangle E less than [#permalink]
07 Dec 2012, 12:41

1

This post received KUDOS

Expert's post

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]
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]
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.

Re: Is the length of a side of equilateral triangle E less than [#permalink]
05 Mar 2014, 00:09

Expert's post

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]
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]
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]
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.

Re: Is the length of a side of equilateral triangle E less than [#permalink]
05 Mar 2014, 23:58

Expert's post

X017in 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.

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 615 times ]

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

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