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

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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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New post 17 Sep 2018, 21:03
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

45% (01:08) correct 55% (01:51) wrong based on 20 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


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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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New post 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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Re: In the figure above, if AB is parallel to DE, DC = EC, what is the per &nbs [#permalink] 18 Sep 2018, 13:47
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In the figure above, if AB is parallel to DE, DC = EC, what is the per

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