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# Is the area of equilateral triangle E less than the area of square C ?

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Math Expert
Joined: 02 Sep 2009
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Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

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04 Dec 2019, 02:49
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Difficulty:

45% (medium)

Question Stats:

59% (01:02) correct 41% (02:03) wrong based on 36 sessions

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Is the area of equilateral triangle E less than the area of square C ?

(1) A side of square C is $$\frac{2}{3}$$ the length of a side of triangle E.

(2) The sum of the perimeters of triangle E and square C is 17

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Re: Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

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04 Dec 2019, 05:30
the question is: is$$\frac{\sqrt{3}}{4}t^2 < s^2$$ ?

from statement (1), $$s = \frac{2}{3}t$$
so $$s^2 = \frac{4}{9}t^2$$ > $$\frac{\sqrt{3}}{4}t^2$$ --> sufficient

from statement (2), 3t+4s = 17 --> clearly insufficient because there is no restrictions for the values

A
Re: Is the area of equilateral triangle E less than the area of square C ?   [#permalink] 04 Dec 2019, 05:30
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