If B is the midpoint of AC, what is the length of BE?

Question

https://gmatclub.com/forum/download/file.php?id=16489 If B is the midpoint of AC, what is the length of BE? (1) doubletr_q1.png

Bunuel · Answer

doubletr_q1.png If B is the midpoint of AC, what is the length of BE? As angle E=Angle D then BE||CD. Now as B is the midpoint of AC and BE||CD then BE becomes a midsegment (a line segment joining the midpoints of two sides of a triangle). The property of midsegemnt: the midsegment is always half the length of the third side . So 2BE=CD. (1) triangles BAE and CAD are 30-60-90 triangles where BE is a midsegment. We know only angles but not the lengths, so can not find BE. Not sufficient. (2) CD = \sqrt{12} --> as 2BE=CD then BE=\frac{CD}{2}=\sqrt{3} . Sufficient. Answer: B. Hope it's clear.

enigma123 · Answer

You are a legend buddy. Top explanation.

madn800 · Answer

Another EASIER way of looking at the problem
(1) we know the angle but not length of any side. Insufficient. Proceed to D

(2)CD=Root 12
 Use property of similarity and we get that triangle ABC is similar to triangle ACD

AC/AB=DC/BE

As B is a midpoint of AC we get 2AB=AC

2AB/AB=Root12/BE

BE=Root12/2

madn800 · Answer

typing mistake above. "proceed to 2" and not "proceed to D"
sorry.

Asifpirlo · Answer

st(2), BE II CD and B is the midpoint.
so BE = 1/2 CD = fixed value.
st(1) provides no fixed value, so insufficient.
Answer (B)

exc4libur · Answer

(1) insufic

(2) sufic

CD/BE=AD/AE
√12/y=x/(x/2)
√12/y=2
y=√12/2=√3

Ans (B)

bumpbot · Answer

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If B is the midpoint of AC, what is the length of BE?

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