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# If an equilateral triangle and a square have the same area, what is th

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Math Expert
Joined: 02 Sep 2009
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If an equilateral triangle and a square have the same area, what is th  [#permalink]

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22 Jan 2018, 01:38
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If an equilateral triangle and a square have the same area, what is the ratio of the side of the square to the side of the triangle?

A. 1 : 2

B. 2 : 3

C. $$\sqrt{3}:4$$

D. $$\sqrt[4]{3}:2$$

E. $$\sqrt[4]{3}:4$$

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If an equilateral triangle and a square have the same area, what is th  [#permalink]

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22 Jan 2018, 01:58
Area of eq triangle = \sqrt{3} / 4 * a*a ( where a is side of eq triangle )
( where a is side of eq triangle) ---------------------- 1

Area of square = s*s
( where s is side of square ) ---------------------- 2

[Given] : eq 1 = eq 2
Inference : s/a = $$\sqrt[4]{3}:2$$

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If an equilateral triangle and a square have the same area, what is th  [#permalink]

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22 Jan 2018, 07:24
Bunuel wrote:
If an equilateral triangle and a square have the same area, what is the ratio of the side of the square to the side of the triangle?

A. 1 : 2

B. 2 : 3

C. $$\sqrt{3}:4$$

D. $$\sqrt[4]{3}:2$$

E. $$\sqrt[4]{3}:4$$

Equilateral triangle has area = $$\frac{\sqrt{3}}{4}*a^2$$ where a - radius of the circle

Similarly, the area of a square with side s = $$s^2$$

Since they have same area $$s^2 = [m]\frac{\sqrt{3}}{4}*a^2$$
s = $$\frac{\sqrt[4]{3}}{2}*a$$

The ratio of the side of the square to the side of the triangle is($$\frac{s}{a}) = \frac{\sqrt[4]{3}}{2}$$(Option D)
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If an equilateral triangle and a square have the same area, what is th   [#permalink] 22 Jan 2018, 07:24
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