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# In the figure above, if AB is parallel to DE, DC = EC, what is the per

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Math Expert
Joined: 02 Sep 2009
Posts: 64068
In the figure above, if AB is parallel to DE, DC = EC, what is the per  [#permalink]

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17 Sep 2018, 21:03
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Difficulty:

65% (hard)

Question Stats:

51% (01:50) correct 49% (01:52) wrong based on 37 sessions

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In the figure above, if AB is parallel to DE, DC = EC, what is the perimeter of triangle DEC?

(1) BE is 5/7 of BC

(2) AC = 13 and AB = 7

Attachment:

image014.jpg [ 1.95 KiB | Viewed 608 times ]

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Re: In the figure above, if AB is parallel to DE, DC = EC, what is the per  [#permalink]

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18 Sep 2018, 13:47
1
given to us is the triangles are similar:
- DEC is Isosceles (due to DC= EC)
- AB || DE

this means the ratios of the sides of the 2 triangles will be the same for all sides
we already have DE, so we need to figure out either DC or EC

(1) BE is 5/7 of BC
while this lets us calculate the ratio, it doesn't tell us anying about the lengtof either of the 2 unknown legs on which we can apply those ratios to try and calculate EC (which we could have done with either the length of BE or BC)

Not suff.

(2) AC = 13 and AB = 7
this gives us the length of the leg of the larger triangle as well as the length of the base of the larger triangle.
while we don't get the ratios here, we can calculate them
we know that the ratio of AB/DE has to be the same as the ratio of AC/DC
so:
7/2 = 13/DC
we can solve this
--> B is sufficient

(just to solve it quickly)
DC = 26/7
so the total perimeter is
66/7 (26/7 + 26/7 + 14/7)

kudos if this helped
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In the figure above, if AB is parallel to DE, DC = EC, what is the per  [#permalink]

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14 Feb 2020, 01:14
Bunuel wrote:

In the figure above, if AB is parallel to DE, DC = EC, what is the perimeter of triangle DEC?

(1) BE is 5/7 of BC

(2) AC = 13 and AB = 7

Attachment:
image014.jpg

Solution

Step 1: Analyse Question Stem

Before moving on to the solution of this problem, we need to know a few properties of triangles.
• Look at the diagram given,

o If $$DE$$ is parallel to $$AB$$, then triangle $$ABC$$ is similar to triangle $$DEC$$.
 Thus, $$\frac{EC}{BC} = \frac{DC}{AC}=\frac{DE}{AB}$$
• Now, by using this property let’s solve the given problem.
o $$AB$$ is parallel to $$DE$$
 Triangle $$ABC$$ is similar to triangle $$DEC$$.
• Thus, $$\frac{EC}{BC}=\frac{DC}{AC}=\frac{DE}{AB}$$
 It is also given that $$DC = EC.$$
 $$DE = 2$$ units
We need to find the perimeter of triangle $$DEC$$.
• $$DE+EC+DC = 2 + EC + DC= 2+2DC$$ [it is given that $$DC = EC$$]
.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: $$BE = \frac{5}{7}*BC$$
• $$\frac{BE}{BC} = \frac{5}{7}$$
o $$1-\frac{BE}{BC} = 1 – \frac{5}{7}$$ [Subtracting both the sides from $$1$$]
o $$\frac{(BC-BE)}{BC} = \frac{2}{7}$$
o EC/BC = 2/7, [BE+EC = BC]
• It means $$\frac{EC}{BC} = \frac{DC}{AC}=\frac{DE}{AB} = \frac{2}{7}$$.
• With this information we can find the ratio of sides, but we cannot find the value of $$DC$$ or $$EC$$.
Hence, statement 1 is not sufficient, we can eliminate answer options A and D.
Statement 2: $$AC = 13$$ and $$AB = 7$$.
• $$\frac{DC}{AC} = \frac{DE}{AB}$$
o $$\frac{DC}{13} = \frac{2}{7}$$
o $$DC = \frac{26}{7}$$
• Perimeter of triangle DEC = $$2 + 2*\frac{26}{7}$$
Hence, statement 2 is sufficient, the correct answer is Option B.
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In the figure above, if AB is parallel to DE, DC = EC, what is the per   [#permalink] 14 Feb 2020, 01:14