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705-805 (Hard)|   Geometry|      
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Right triangle ABC has leg lengths AB=20 and BC=21. Including AB and B 17 Nov 2018, 10:00
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42% (02:43) correct 58% (03:06) wrong based on 45 sessions

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GMATbuster's Weekly Quant Quiz#9 Ques #1


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Right triangle ABC has leg lengths AB=20 and BC=21. Including AB and BC, how many line segments with integer length can be drawn from vertex B to a point on hypotenuse AC?
A) 5
B) 8
C) 12
D) 13
E) 15
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D

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Right triangle ABC has leg lengths AB=20 and BC=21. Including AB and B 19 Nov 2018, 06:50
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Right triangle ABC has leg lengths AB=20 and BC=21. Including AB and B 17 Nov 2018, 10:05
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Hypotenuse = sqrt (20*20 + 21*21) = sqrt(841) = 29

0.5*20*21 = 0.5*29*BP
BP = 14.48 approx

So, integer values between 14.48 and 20 inclusive = 15,16,...20 = 6 integers
Between 14.8 and 21 inclusive = 15,16,....21 = 7 integers

Total = 13
Option D
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Right triangle ABC has leg lengths AB=20 and BC=21. Including AB and B 17 Nov 2018, 10:23
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Length of AC: √{(20x20+21x21}= 29
Area of ABC: 1/2(20)(21)
Consider the perpendicular to AC to be x. This will be the shortest length
Thus
1/2 (29)(x)= 1/2(20)(21)
x= (20)(21)/29= 14.48
Thus number of line segments with integer lengths:
(15 to 21) = 7 towards BC & (15-20)= 6 towards AB
Hence total 13 line segments
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Right triangle ABC has leg lengths AB=20 and BC=21. Including AB and B 15 Dec 2025, 10:25
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