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If an equilateral triangle and a square has an equal face of 12 inches. Find the quantitative relation between their areas.

4 : √3
2 : √3
2 : 3
1 : √3
Explanation:

Area of a square with side a = $a^{2}$
Here, a = 12 inches then $a^{2}$ = 144
Area of an equilateral triangle with side b = ($sqrt^{3}$)($b^{2}$)/4.
Here, b = 12 inches then (sqrt3)($b^{2}$)/4 = (sqrt3)(144)/4 = 36(sqrt3)
Now, the required relation = Area of the square / Area of the triangle
= 144 / [(sqrt3)36] = 4/sqrt3.

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