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

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