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Triangle ABC is right angled at B, while triangle ACD is right angled

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Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

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22 Nov 2018, 23:38
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Difficulty:

85% (hard)

Question Stats:

29% (01:45) correct 71% (01:55) wrong based on 64 sessions

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Triangle ABC is right angled at B, while triangle ACD is right angled at C. Is the length of CD > length of AB?

(1) Angle BAC = 45 degrees.

(2) Angle ADC = 45 degrees.
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Joined: 02 Aug 2009
Posts: 7686
Re: Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

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23 Nov 2018, 20:02
1
amanvermagmat wrote:
Triangle ABC is right angled at B, while triangle ACD is right angled at C. Is the length of CD > length of AB?

(1) Angle BAC = 45 degrees.

(2) Angle ADC = 45 degrees.

So we have a triangle ABC where AC is the hypotenuse and in other triangle AC is a side.
1) angle BAC =45
So triangle BAC is isosceles right angled triangle.
Nothing about D, we could take D to any length
Insufficient

So triangle ADC is a right angled triangle with AC=CD
But in other triangle AC is the hypotenuse so it is >the side AB..
Therefore CD is also greater than AB
Sufficient

B
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PicsArt_11-24-08.27.50.jpg [ 35.33 KiB | Viewed 491 times ]

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Re: Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

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29 Nov 2018, 01:10
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Hello,

Since the triangles mentioned in the problem are right-angled triangles, it is natural to think that applying the Pythagoras theorem will help us solve the problem. However, we just need to know the concept that the Hypotenuse is the longest side in a right-angled triangle, to be able to solve this problem.

Using statement 1 alone,

We can say that triangle ABC is an isosceles right-angled triangle and hence, AB = BC. However, this is grossly insufficient to find out a relationship between CD and AB, since we know neither the lengths of the sides of the triangle ACD nor the angles. Hence, statement I alone is insufficient.

Using statement II alone,

We can deduce that triangle ACD is now an isosceles right-angled triangle and hence, CD = AC. Now, in triangle ABC, AC represents the hypotenuse and is, therefore, the longest side in triangle ABC. Hence, it has to be longer than AB; so we can say that CD is definitely longer than AB. Statement II alone is sufficient.

Therefore, the answer option is B.

In such questions, a good thing to do is to draw a diagram and try to put in as many values as possible, before analysing it further. Also, a point to remember about DS questions on Geometry is that any data that gives you a UNIQUE figure/diagram is the data that is going to be sufficient and vice versa.

Hope this helps!

Cheers,
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Triangle ABC is right angled at B, while triangle ACD is right angled - 2.jpg [ 63.51 KiB | Viewed 356 times ]

Triangle ABC is right angled at B, while triangle ACD is right angled - 1.jpg [ 73.46 KiB | Viewed 358 times ]

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Re: Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

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29 Nov 2018, 09:34
amanvermagmat wrote:
Triangle ABC is right angled at B, while triangle ACD is right angled at C. Is the length of CD > length of AB?

(1) Angle BAC = 45 degrees.

(2) Angle ADC = 45 degrees.

Need to draw a picture to answer this question.

S1) Easy to see from the image that point D can be moved anywhere you want, so length of CD can be anything. Insufficient
S2) ACD is a 45:45:90, so CD = AC. AC is hypotenuse of ABC so AC > AB. Therefore CD > AB. Answer definitively is yes. Sufficient

Re: Triangle ABC is right angled at B, while triangle ACD is right angled   [#permalink] 29 Nov 2018, 09:34
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