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# Is the height of equilateral triangle B greater than the diagonal of

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Is the height of equilateral triangle B greater than the diagonal of  [#permalink]

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06 Sep 2018, 00:27
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Difficulty:

45% (medium)

Question Stats:

65% (01:40) correct 35% (01:58) wrong based on 27 sessions

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Is the height of equilateral triangle B greater than the diagonal of square D?

(1) (Length of a side of B)/(Length of a side of D) = 1

(2) The area of triangle B is 3.89 and the area of square D is 9.

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Is the height of equilateral triangle B greater than the diagonal of  [#permalink]

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06 Sep 2018, 04:08
Bunuel wrote:
Is the height of equilateral triangle B greater than the diagonal of square D?

(1) (Length of a side of B)/(Length of a side of D) = 1

(2) The area of triangle B is 3.89 and the area of square D is 9.

Question: Is the height of equilateral triangle B greater than the diagonal of square D?

Height of Equilateral = $$(√3/2)a$$ . where a is the side of equilateral
Diagonal of square = $$x√2$$ where x is the side of the square

Is $$(√3/2)a > x√2$$

Is $$a/x > √(8/3)$$?

Statement 1: (Length of a side of B)/(Length of a side of D) = 1

i.e. $$a/x = 1$$ Exact value of ratio hence

SUFFICIENT

Statement 2: The area of triangle B is 3.89 and the area of square D is 9

$$(√3/4)a^2 = 3.89$$

$$x^2 = 9$$

Exact value of ratio $$a/x$$ hence

SUFFICIENT

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Is the height of equilateral triangle B greater than the diagonal of   [#permalink] 06 Sep 2018, 04:08
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