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

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Bunuel
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In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, [#permalink] New post   21 Sep 2018, 01:14
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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

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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, [#permalink] New post   21 Sep 2018, 01:20
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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

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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

Answer: Option E
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BrentGMATPrepNow
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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, [#permalink] New post   21 Sep 2018, 08:31
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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

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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

Answer: E

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In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, [#permalink] New post   11 Mar 2023, 20:15
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This question tests our understanding about similar triangles, it’s mentioned in the stem that line de and AC are parallel,the first assumption added must me the triangles are similar, the second assumption is about the unknown side, we can label be as x and using algebra we can solve for the value of x base of abc/height of abc= base of bde/height of bde = x+2/12 = x/8 ( mentioned un the stem ad =2, we can deduce that ec =2), solving x=4 side bc = 4+2 =6
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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, [#permalink] New post   22 Sep 2018, 04:14
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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.

Answer: E
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Re: In the figure above, DE and AC are parallel lines. If AC = 12, DE = 8, [#permalink] New post   23 Sep 2018, 08:44
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] New post   23 Sep 2018, 08:57
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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, [#permalink] New post   06 Apr 2024, 09:27
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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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