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03 Nov 2020, 04:13
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (02:05) correct
25%
(02:23)
wrong
based on 57
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Not Attempted Yet
If BD=DC, \( \angle DBC=30\) and DE=EC=5, what is the length of BE?
(A) \(5\)
(B) \(5\sqrt{2}\)
(C) \(7\)
(D) \(10\)
(E) \(10\sqrt{2}\)
Chetan's questions
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03 Nov 2020, 09:05
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chetan2u
A very nice question.
In triangle BDC, Since BD = DC, therefore \(\angle{DBC} = \angle{DCB} = 30^o\). (Angles opposite equal sides are equal)
In Triangle DEC, given DE = EC, therefore \(\angle{EDC} = \angle{DCB} = 30^o\) (Angles opposite equal sides are equal)
Therefore, \(\angle{EDC} = 60^o\), since it is the exterior angle of triangle DEC, and the exterior angle = sum of opposite interior angles.
Triangle BDE is a 30 - 60 - 90 triangle, and the ratio of the sides opposite the angles 30 - 60 - 90 = 1 : \(\sqrt{3}\) : 2
Side opposite \(30^o\) = DC = 5 and BE is the side opposite \(90^o\)
Therefore \(\frac{DE}{BE} = \frac{1}{2}\)
BE = 2 * 5 = 10
Option D
Arun Kumar
03 Nov 2020, 17:33
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chetan2u
\(\angle EDC = \angle C = \angle DBC = 30\). From the supplementary angle theorem we have \(\angle DEB = \angle EDC + \angle C = 30 + 30 = 60.\)
Now focus on \(\triangle BDE\), it has a 30 degree angle and a 60 degree angle so the missing angle \(\angle BDE\) is a right angle. Then this triangle is a 30 degree right triangle. DE = 5 so BE = 2*DE = 10.
Ans: D
