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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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05 Sep 2016, 10:09
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
If in the figure above, AD=DB and DE=√2, what is the length of line se [#permalink]
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05 Sep 2016, 11:50
1
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
(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
+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.
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..
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
Answer: B
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If in the figure above, AD=DB and DE=√2, what is the length of line se
[#permalink]
08 Mar 2018, 18:12