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# If side BE has length 10 and side AC has length

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Manager
Joined: 13 Apr 2010
Posts: 87

Kudos [?]: 6 [0], given: 11

If side BE has length 10 and side AC has length [#permalink]

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22 Oct 2017, 03:16
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Difficulty:

45% (medium)

Question Stats:

78% (01:28) correct 22% (02:12) wrong based on 27 sessions

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If side BE has length 10 and side AC has length 8, what is the area of the triangle BOC ?

A. $$2\sqrt{3}$$
B. $$4\sqrt{3}$$
C. $$6\sqrt{3}$$
D. $$8\sqrt{3}$$
E. $$12\sqrt{3}$$
[Reveal] Spoiler: OA

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triangle BOC.JPG [ 16.78 KiB | Viewed 330 times ]

Kudos [?]: 6 [0], given: 11

Math Expert
Joined: 02 Aug 2009
Posts: 5341

Kudos [?]: 6107 [2], given: 121

If side BE has length 10 and side AC has length [#permalink]

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22 Oct 2017, 07:36
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sb0541 wrote:
If side BE has length 10 and side AC has length 8, what is the area of the triangle BOC ?

A. $$2\sqrt{3}$$
B. $$4\sqrt{3}$$
C. $$6\sqrt{3}$$
D. $$8\sqrt{3}$$
E. $$12\sqrt{3}$$

A very SIMPLE solution..

Triangle BOC is 30-60-90 angle with right angle at O...
HOW?

Angle DEB=60=AngleABE ( Alternate angles)..
so check triangle DBO
angle ABO = 60.... angle BAO = 30 so ANGLE BOA = 180-60-30=90...
so BE and AC intersect at 90..

therefore Triangle OBC is 90 at O...
Now check triangle ABC ( 30-60-90), sides are in ratio $$1:\sqrt{3}:2$$
hyp = ratio of 2 in $$1:\sqrt{3}:2$$ so BC = $$\frac{8}{2}=4$$

Now OBC is also 30-60-90 where hypotenuse is 4, so other two sides = $$\frac{4}{2}$$ and $$\frac{4}{2}*\sqrt{3}$$..
so $$AREA = \frac{1}{2}*\frac{4}{2}*\frac{4}{2}*\sqrt{3} = 2*\sqrt{3}$$

A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6107 [2], given: 121

If side BE has length 10 and side AC has length   [#permalink] 22 Oct 2017, 07:36
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