If the medians of two equilateral triangles are in the ratio 3 : 2, th – InterviewSolution

1.

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

Answer»

(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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