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# CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ?

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Math Expert
Joined: 02 Sep 2009
Posts: 42606

Kudos [?]: 135613 [0], given: 12705

CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ? [#permalink]

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29 Oct 2017, 00:26
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Difficulty:

25% (medium)

Question Stats:

85% (00:56) correct 15% (00:57) wrong based on 41 sessions

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CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

[Reveal] Spoiler:
Attachment:

2017-10-29_1225.png [ 5.54 KiB | Viewed 398 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135613 [0], given: 12705

VP
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [0], given: 645

CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ? [#permalink]

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29 Oct 2017, 08:23
Bunuel wrote:

CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

[Reveal] Spoiler:
Attachment:
The attachment 2017-10-29_1225.png is no longer available

Attachment:

tri.png [ 7.32 KiB | Viewed 269 times ]

Rotate the triangle clockwise 90 degrees.

∆ ACD is similar to triangle AEF:

Their bases (DC and FE) are parallel.

Those parallel lines are cut by transversals (sides AF and AE of the larger triangle).

∠ D = ∠F (corresponding)
∠ C = ∠E (corresponding)

Both triangles share ∠ A

By AAA, they are similar triangles, whose corresponding sides have the same ratio
Small side $$AD$$ corresponds to large side $$AF$$. Small side $$DC$$ corresponds to large side $$EF$$

$$AD = 3$$, $$CD = 4$$

For small ∆ ACD, $$\frac{side}{side} = \frac{AD}{DC}=\frac{3}{4}$$

That ratio will hold for larger ∆ AEF

$$AD = DF = 3$$
So side $$AF = 6$$
Let side $$EF = x$$

$$(\frac{AD}{DC}=\frac{AF}{EF})=(\frac{3}{4}= \frac{6}{x})=\frac{6}{8}$$

$$EF = 8$$

Kudos [?]: 402 [0], given: 645

Intern
Joined: 22 Jun 2017
Posts: 17

Kudos [?]: 3 [0], given: 35

Location: Italy
GPA: 3.64
CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ? [#permalink]

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31 Oct 2017, 07:34
Bunuel wrote:

CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

[Reveal] Spoiler:
Attachment:
2017-10-29_1225.png

since AD=DF and CD is parallel to EF, CD is the midsegment of the triangle, and EF is equal 2 times the midsegment, so IMO the answer is E

Kudos [?]: 3 [0], given: 35

CD is parallel to EF. AD = DF, CD = 4, and DF = 3. What is EF ?   [#permalink] 31 Oct 2017, 07:34
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