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# In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8,

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In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8,  [#permalink]

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21 Sep 2018, 00:14
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Difficulty:

45% (medium)

Question Stats:

62% (01:46) correct 38% (01:06) wrong based on 65 sessions

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In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, and AD = 2, what is the length of AB?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Attachment:

Capture.JPG [ 20.93 KiB | Viewed 736 times ]

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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8,  [#permalink]

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21 Sep 2018, 00:20
Bunuel wrote:

In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, and AD = 2, what is the length of AB?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Attachment:
Capture.JPG

Since bases of the triangles are parallel hence, Triangles ABC and DBE are similar triangle and Let, AB = x

i.e. AC/DE = AB/DB

i.e. 12/8 = x/(x-2)
i.e. x = 6

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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8,  [#permalink]

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21 Sep 2018, 07:31
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Top Contributor
Bunuel wrote:

In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, and AD = 2, what is the length of AB?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Attachment:
Capture.JPG

DE and AC are parallel lines, we have 2 pairs of equal angles

Let x = the length of BD and add in the other given lengths

At this point, we can see that there are two SIMILAR TRIANGLES within the diagram.
They are shown separately below.

KEY CONCEPT: The ratios of any two pairs of corresponding sides are always equal.

Sides DE and AC are corresponding, and sides BD and BA are corresponding
So, we can write: 8/12 = x/(x+2)
Cross multiply go get: (8)(x+2) = (12)(x)
Expand: 8x + 16 = 12x
We get: 16 = 4x
Solve: x = 4

Since side AB has length x + 2, we can conclude that the length of side AB = 4 + 2 = 6

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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8,  [#permalink]

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22 Sep 2018, 03:14

Solution

Given:
• In the given figure, DE || AC
• AC = 12, DE = 8, and AD = 2

To find:
• The length of AB

Approach and Working:
As DE || AC, angle BDE = angle BAC and angle BED = angle BCA

Hence, if we consider triangles BDE and BAC,
• angle BDE = angle BAC
• angle BED = angle BCA
• angle B is common to both triangles

So, the triangles are similar to each other.

Therefore, $$\frac{BD}{BA} = \frac{DE}{AC}$$
• Or, $$\frac{AB – AD}{AB} = \frac{DE}{AC}$$
• Or, $$1 – \frac{2}{AB} = \frac{8}{12}$$
• Or, $$\frac{2}{AB} = \frac{1}{3}$$
• Or, AB = 2 x 3 = 6

Hence, the correct answer is option E.

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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8,  [#permalink]

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23 Sep 2018, 07:44
this problem does not have sense. It is imposible that the side is 6 and half the base also 6. NO SENSE!!!
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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8,  [#permalink]

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23 Sep 2018, 07:57
Top Contributor
MartyKaan wrote:
this problem does not have sense. It is imposible that the side is 6 and half the base also 6. NO SENSE!!!

I'm not sure I understand what you're saying.
There are infinitely many triangles in which the length of one side is half the length of one of the other sides.
For example, all 30-60-90 triangles have this feature.
One such 30-60-90 triangle could have lengths 1, 2 and √3

That said, it's possible I've misinterpreted your response. If so, please elaborate.

Cheers,
Brent
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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, &nbs [#permalink] 23 Sep 2018, 07:57
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