In an equilateral triangle ΔABC, D divides BC in the ratio 2 : 1 while E divide

Question

In an equilateral triangle ΔABC, D divides BC in the ratio 2 : 1 while E divides AC in the ratio 1 : 2. Find BE : ED ?

Options:

A . 4:3

B . 2:√3

C . √7:√3

D . Cannot be determined

Answer: Option C
:
C

Let the side of the equilateral triangle ΔABC be 3 units. Clearly, BD = 2, CD = 1 and CE = 2.
CD/CE =

\frac{1}{2}

∠

DEC=30

^{\circ}

Hence, ΔCDE is a right angled triangle.
Similarly, ΔBDE is also a right angled triangle.
BE =

\sqrt{7}

and ED =

\sqrt{3}

hence BE:ED =

\sqrt{7}

\sqrt{3}

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