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

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

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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. \(\sqrt[4]{3}:4\)
[Reveal] Spoiler: OA

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

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New post 22 Jan 2018, 00:58
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 = \(\sqrt[4]{3}:2\)

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

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New post 22 Jan 2018, 06:24
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, 06:24
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