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Math Expert V
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If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 40% (01:42) correct 60% (01:45) wrong based on 212 sessions

### HideShow timer Statistics  If in the figure above, AD=DB and DE=√2, what is the length of line segment AC?

(1) x=45

(2) DE||AC

Attachment: T6372.png [ 5.2 KiB | Viewed 4398 times ]

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If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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1
I think ans is B. We can use ratio of sides for similar triangles

AB/DB = AC/DE

2*DB/DB = AC/sqrt(2)

AC=2*sqrt(2)

why do we need exact values of angles? Isn't it enough to know which angles are equal? Please let me know where I am missing.

B

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##### General Discussion
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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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1. If X=45, making triangle DEB an isosceles triangle. We know that an isosceles right triangle has side in the ratio 1:1:sqrt(2) . Hence, DB = AD = BE = EC = 1. Hence, we can find the measure of AC(using Pythagoras theorem). Hence, it is sufficient

2. DE being parallel to AC, doesn't lead to finding the measure of AC. This statement is not sufficient! Hence, the answer is option A

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If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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pushpitkc wrote:
1. If X=45, making triangle DEB an isosceles triangle. We know that an isosceles right triangle has side in the ratio 1:1:sqrt(2) . Hence, DB = AD = BE = EC = 1. Hence, we can find the measure of AC(using Pythagoras theorem). Hence, it is sufficient

2. DE being parallel to AC, doesn't lead to finding the measure of AC. This statement is not sufficient! Hence, the answer is option A

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Attachment: T6372.png [ 7.48 KiB | Viewed 3796 times ]

is still EC be 1??
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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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Bunuel wrote: If in the figure above, AD=DB and DE=√2, what is the length of line segment AC?

(1) x=45

(2) DE||AC

Attachment:
T6372.png

(1) not suff.. as we dont have idea of length EC
(2) not suff..although triangles ABC & DBE were similar we have no idea of sides DB and BE(triangle DBE could be 30-60-90 or 45-45-90)

Combining Both
As DBE is isosceles sides are known and DE||AC both triangles ABC & DBE were similar thus we know all sides of ABC

Ans C
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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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Bunuel wrote: If in the figure above, AD=DB and DE=√2, what is the length of line segment AC?

(1) x=45

(2) DE||AC

Attachment:
T6372.png

+1 for C ) Both are required and neither one of them is self-sufficient.

1) this just tells that smaller one is Isosceles but not about the larger one. No reason to assume that these 2 are similar.
2) this tells these 2 are similar, but nothing about the angle.

1) + 2) tells that these are similar and Isosceles.
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If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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acegmat123 wrote:
I think ans is B. We can use ratio of sides for similar triangles

AB/DB = AC/DE

2*DB/DB = AC/sqrt(2)

AC=2*sqrt(2)

why do we need exact values of angles? Isn't it enough to know which angles are equal? Please let me know where I am missing.

B

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Great catch Actually u r right ..there is no need of statement (1)
both triangles are similar and one side is double the other is given and we know value of second side.
thus AC=2*sqrt(2)
Thus B is suff..

Ans B
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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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ll lines will themselves make the triangles similar. hence, we don't need any angles. We have the ratio of one sides, we can find the required values.

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If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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from statement 2 :- DBE and ABC are similar triangles
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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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acegmat123 wrote:
I think ans is B. We can use ratio of sides for similar triangles

AB/DB = AC/DE

2*DB/DB = AC/sqrt(2)

AC=2*sqrt(2)

why do we need exact values of angles? Isn't it enough to know which angles are equal? Please let me know where I am missing.

B

You're right, I completely missed the SAS rule of Triangle.
+1 for you.
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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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Bunuel wrote: If in the figure above, AD=DB and DE=√2, what is the length of line segment AC?

(1) x=45

(2) DE||AC

Attachment:
T6372.png

from 1 insuff

from 2 and stem

DE is midsegment and it is equal 1/2 AC therefore AC could be found.... suff
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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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St. (1) Not sufficient. We only know that the sides of the smaller triangle are 1 & 1.
No info about the relation of the smaller triangle to ABC.

St. (2) DE || AC. Bingo. Similar triangles.
DB/DE=AB/AC
=>(AB/2)/sqrrt2=AB/AC .... => AC=2*sqrrt2 Sufficient.

Ans. B
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If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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Top Contributor
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Bunuel wrote: If in the figure above, AD=DB and DE=√2, what is the length of line segment AC?

(1) x = 45

(2) DE || AC

Attachment:
T6372.png

Target question: What is the length of line segment AC?

Given: AD = DB and DE = √2

Statement 1: x = 45
IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video at the bottom of this post.

If x = 45°, then ∠DEB is 45° since all 3 angles in ∆BED must add to 180°
Since we also know that DE = √2, we can see that ∆BED is LOCKED into just one triangle. However, even though ∆BED is LOCKED into just one triangle, vertex C is not locked into place.
In fact, we can mentally "grab" point C and pull it left and right without affecting ∆BED (see below) This means that statement 1 does NOT lock in the length of side AC
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: DE || AC
If lines DE and AC are parallel, we get the following equal angles. Since ∆BED and ∆BCA share the same 3 angles, we can conclude that ∆BED and ∆BCA are SIMILAR TRIANGLES Also notice that, since AD = DB, we can conclude that side AB is twice as long as side DB
This means ∆BED is twice as big as ∆BCA
So, if DE = √2, then it's corresponding side, AC, must be twice as long.
So, side AC must have length 2√2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO

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Re: If in the figure above, AD=DB and DE=√2, what is the length of line se  [#permalink]

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_________________ Re: If in the figure above, AD=DB and DE=√2, what is the length of line se   [#permalink] 19 Jun 2019, 04:55
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