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In the figure above, DE is parallel to AC. BE = 2EC DE = 12
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26 Sep 2018, 15:03
26 Sep 2018, 15:03
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50% (01:12) correct
49% (01:16) wrong based on 89 sessions
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In the figure above, DE is parallel to AC.
BE = 2EC
DE = 12
Quantity A |
Quantity B |
AC |
18 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: In the figure above, DE is parallel to AC. BE = 2EC DE = 12
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12 Aug 2019, 21:10
12 Aug 2019, 21:10
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Since, DE and AC are parallel , we can say that the inner (smaller) triangle is a fraction of the outer triangle and ratios of each corresponding sides of the triangles are equal
Therefore we can write , BE/BC = DE/AC
=> 2EC/3EC = 12/AC
=> 2AC = 36
=> AC = 18
Answer is C
Therefore we can write , BE/BC = DE/AC
=> 2EC/3EC = 12/AC
=> 2AC = 36
=> AC = 18
Answer is C
Re: In the figure above, DE is parallel to AC. BE = 2EC DE = 12
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09 Nov 2019, 01:11
09 Nov 2019, 01:11
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Official Explanation
If AC is parallel to DE, then triangles DBE and ABC are similar. If BE = 2EC then if EC is set to equal x, BE would equal 2x and BC would equal x + 2x, or 3x. That means that the big triangle is in a 3 : 2 ratio with the small triangle (since BC : BE = 3x : 2x). Set up the proportion for the bottom sides of these triangles, both of which are opposite the shared vertex at B:
\(\frac{2}{3}\) = \(\frac{DE}{AC}\)
\(\frac{2}{3}\)= \(\frac{12}{AC}\)
2(AC) = 36
AC = 18
The two quantities are equal.
If AC is parallel to DE, then triangles DBE and ABC are similar. If BE = 2EC then if EC is set to equal x, BE would equal 2x and BC would equal x + 2x, or 3x. That means that the big triangle is in a 3 : 2 ratio with the small triangle (since BC : BE = 3x : 2x). Set up the proportion for the bottom sides of these triangles, both of which are opposite the shared vertex at B:
\(\frac{2}{3}\) = \(\frac{DE}{AC}\)
\(\frac{2}{3}\)= \(\frac{12}{AC}\)
2(AC) = 36
AC = 18
The two quantities are equal.
