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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the figure above, if AB is parallel to DE, DC = EC, what is the per

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Math Expert V
Joined: 02 Sep 2009
Posts: 64249
In the figure above, if AB is parallel to DE, DC = EC, what is the per  [#permalink]

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Difficulty:   65% (hard)

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

### HideShow timer Statistics 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 610 times ]

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IESE School Moderator S
Joined: 11 Nov 2017
Posts: 145
Location: Belgium
Concentration: Technology, Operations
GMAT 1: 670 Q47 V34
GMAT 2: 750 Q50 V41 GMAT 3: 750 Q50 V41 GPA: 2.5
WE: Engineering (Aerospace and Defense)
Re: In the figure above, if AB is parallel to DE, DC = EC, what is the per  [#permalink]

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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
GMATWhiz Representative G
Joined: 07 May 2019
Posts: 709
Location: India
In the figure above, if AB is parallel to DE, DC = EC, what is the per  [#permalink]

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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  