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The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 06:07
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The three sides of an acute angled triangle (all in cms) are 12, 19 and x. How many integer values can x take?A. 23 B. 22 C. 15 D. 8 E. 7
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The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 06:38
In acute angle triangles all angles in the triangle should be less than 90. The maximum length of x can be when it is the hypotenuse of the triangle. So, x= sqrt(12^2 + 19^2) = 22.5 (approx) The maximum length of x can be when side of length 12 is the hypotenuse of the triangle. So, x = sqrt (19^2  12^2) = 14.7 (approx) So, x>14.7 and x<22.5.
Hence, possible values for x can be 15,16,17,18,19,20,21 and 22. Total 8 values.Answer D. P.S. Don't forget to give kudos
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 07:15
Hi, Thank you for the prompt response!! A follow up question please Should the Third paragraph read  The Minimum length of X can be when 19 is the Hypotenuse of the Triangle? Do correct me if I am wrong here. Sent from my iPhone using GMAT Club Forum mobile app
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 08:27



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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 10:59
For all triangle any side is greater than the difference of other two and less that the sum so 12+19 = 31 1219=7 so 7<x<31=(317)+1 23
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 11:12
Hi LogicGuru1, Pls refer to the links shared by Bunuel above. It has indepth discussion on this topic. I am sure, you will find it useful! Sent from my iPhone using GMAT Club Forum mobile app
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 11:15
Hi Abhishek, The catch here is "Acute triangle". So we need to do two steps of calculations. Pls refer to above responses by Bunuel and 14101992. Sent from my iPhone using GMAT Club Forum mobile app
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 11:15
14101992 wrote: In acute angle triangles all angles in the triangle should be less than 90. The maximum length of x can be when it is the hypotenuse of the triangle. So, x= sqrt(12^2 + 19^2) = 22.5 (approx) The maximum length of x can be when side of length 12 is the hypotenuse of the triangle. So, x = sqrt (19^2  12^2) = 14.7 (approx) So, x>14.7 and x<22.5.
Hence, possible values for x can be 15,16,17,18,19,20,21 and 22. Total 8 values.Answer D. P.S. Don't forget to give kudos By definition an acute triangle is one that has all three internal angles less than 90 degrees [/u] Aren't you using Pythagorus theorem which is only and exclusively meant for right triangle. (having one intnernal angle that measure exactly 90 degrees )
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 11:52
14101992 wrote: In acute angle triangles all angles in the triangle should be less than 90. The maximum length of x can be when it is the hypotenuse of the triangle. So, x= sqrt(12^2 + 19^2) = 22.5 (approx) The maximum length of x can be when side of length 12 is the hypotenuse of the triangle. So, x = sqrt (19^2  12^2) = 14.7 (approx) So, x>14.7 and x<22.5.
Hence, possible values for x can be 15,16,17,18,19,20,21 and 22. Total 8 values.Answer D. P.S. Don't forget to give kudos You mean one maximum and one minimum right? Posted from my mobile device



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Re: The three sides of an acute angled triangle12,19&X. How many X?
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26 Jun 2016, 21:11
LogicGuru1You are right. Pythagoras theorem is used for only right angle triangles and a right angle triangle has one angle as 90 and rest two <90. Now, you are given to find out the all possible acute angle triangles. Acute angle triangle will have all angles less than 90. So, by using Pythagoras theorem, we will have hypotenuse of that length where an angle of the triangle will be 90 and rest 2 angles less than 90. Now, as you can see in my previous post, x>14.7 and x<22.5 and not x≥14.7 and x≤22.5. If I would have taken the latter, then I would be including the triangles with one angle as 90 degrees. But, since I have taken the former, it will only give me values of x for which all angles will be less than 90. I hope I am able to solve your query. paidlukkhaThe option A will include many triangle which have one of the angles that are greater than 90. Kindly go through the solution one more time. You will be able to get it.  P.S. Don't forget to give kudos
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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Re: The three sides of an acute angled triangle12,19&X. How many X?
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