Vincen wrote:If an equilateral triangle and a square have the same area then , what is the ratio of the side of the square to the side of the triangle?
(A) 1 : 2
(B) 2 : 3
(C) √3 : 4
(D) ∜3 : 4
(E) ∜3 : 2
Area of an equilateral triangle = (s²√3)/4.
Let the square have a side of 1, with the result that the area of the square = 1² = 1.
Since the equilateral triangle has the same area, we get:
(s²√3)/4 = 1
s² = 4/√3
s = 2/(∜3).
Resulting ratio:
(side of the square)/(side of the triangle) = 1/(2/(∜3)) = (∜3)/2.
The correct answer is
E.
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