Question

In an equilateral triangle $\Delta$ABC, D divides BC in the ratio 2 : 1 while E divides AC in the ratio 1 : 2. Find BE : ED.

• A. 4:3
• B.
• C.
• D. Cannot be determined

Answer 1

The correct option is C

Let the side of the equilateral triangle $\Delta$ABC be 3 units. Clearly, BD = 2, CD = 1 and CE = 2.

CD/CE = $\frac{1}{2}$ So $\angle$DEC=30${}^{\circ }$

Hence, $\Delta$CDE is a right angled triangle.

Similarly, $\Delta$BDE is also a right angled triangle.

BE = $\sqrt{7}$ and ED = $\sqrt{3}$ hence BE:ED = $\sqrt{7}$ : $\sqrt{3}$