ratio of areas problem

Geometry Level 1

Four identical equilateral triangles are arranged as shown so that a square is formed at the center. Find the ratio of the area of the square to the areas of the four equilateral triangles.

1 3 \dfrac{1}{\sqrt{3}} 1 3 \dfrac{1}{3} 1 2 \dfrac{1}{\sqrt{2}} 1 5 \dfrac{1}{5}

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1 solution

Aaryan Maheshwari
Dec 15, 2017

a 2 : 4 × 3 4 a 2 a^2:4\times\dfrac{\sqrt{3}}{4}\space a^2 = a 2 : 3 a 2 =a^2:\sqrt{3}a^2 = 1 : 3 =\boxed{1:\sqrt{3}}

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