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If the medians of two equilateral triangles are in the ratio 3 : 2, then what is the ratio of their sides?

(a) 1 : 1 

(b) 2 : 3 

(c) 3 : 2 

(d) √3: √2

1 Answer

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(c) 3 : 2

Median of an equilateral triangle = \(\frac{\sqrt2}{2}\) x side

Let the sides of the two equilateral triangles be a1 and a2 respected. Then,

\(\frac{\frac{\sqrt3}{2}a_1}{\frac{\sqrt3}{2}a_2}\) = \(\frac32\) ⇒ \(\frac{a_1}{a_2}\) = \(\frac32\).

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