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:

\sqrt{3}

C .

\sqrt{7}

\sqrt{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 = $\frac{1}{2}$ So $∠$ 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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