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In right triangle LMN, the ratio of the longest side to the shortest

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Bunuel
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In right triangle LMN, the ratio of the longest side to the shortest [#permalink] New post   20 Nov 2018, 00:56
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In right triangle LMN, the ratio of the longest side to the shortest side is 5 to 3. If the area of LMN is between 50 and 150, which of the following could be the length of the shortest side?Indicate all possible values.

I. 9
II. 12
III. 15

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
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D
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tomomnomnom
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Re: In right triangle LMN, the ratio of the longest side to the shortest [#permalink] New post   20 Nov 2018, 02:06
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If LMN is a right triangle with a longest side of 5x and a shortest side of 3x, the remaining side needs to be 4x (Pythagorean tiplet, ratio 3-4-5).
That being said, we can plug in I, II and III for the shortest side to find the area of the triangle and determine whether the requirement of 50 < area LMN < 150 is met.

I: (9*12)/2 = 54
II: (12*16)/2 = 96
III: (15*20)/2 = 150

Thus, only I and II are possible values for the shortest side. Answer is D.

Please let me know if I missed something. I might be on the completely wrong track.
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Re: In right triangle LMN, the ratio of the longest side to the shortest [#permalink] New post   20 Nov 2018, 09:36
tomomnomnom wrote:
If LMN is a right triangle with a longest side of 5x and a shortest side of 3x, the remaining side needs to be 4x (Pythagorean tiplet, ratio 3-4-5).
That being said, we can plug in I, II and III for the shortest side to find the area of the triangle and determine whether the requirement of 50 < area LMN < 150 is met.

I: (9*12)/2 = 54
II: (12*16)/2 = 96
III: (15*20)/2 = 150

Thus, only I and II are possible values for the shortest side. Answer is D.

Please let me know if I missed something. I might be on the completely wrong track.


tomomnomnom : you have done correct , but why have you marked option D , infact all three options satisfy the requirement of area >50 and < 150 ... option E is correct..
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In right triangle LMN, the ratio of the longest side to the shortest [#permalink] New post   20 Nov 2018, 10:01
Archit3110
Hi Archit, I interpreted "between 50 and 150" as 50<area LMN<150. Thus, III, leading to an area of 150 exactly, would not be in the range. If, however, the correct translation would have been 50≤area LMN≤150, then the answer would indeed be E. Was my assumption wrong?
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Archit3110
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In right triangle LMN, the ratio of the longest side to the shortest [#permalink] New post   20 Nov 2018, 10:07
tomomnomnom wrote:
Archit3110
Hi Archit, I interpreted "between 50 and 150" as 50<area LMN<150. Thus, III, leading to an area of 150 exactly, would not be in the range. If, however, the correct translation would have been 50≤area LMN≤150, then the answer would indeed be E. Was my assumption wrong?



tomomnomnom we need to find areas which are between range of 50-150 so following are the areas:

1(9*12)/2 = 54
II: (12*16)/2 = 96
III: (15*20)/2 = 150

and all are falling under range of 50-150 would be correct , yes it would 1 & 2 only .. 3rd not to be included... my bad i misunderstood the range to be 50-154... :( i get dyslexic attacks sometimes i feel... god help me on D day...
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Re: In right triangle LMN, the ratio of the longest side to the shortest [#permalink] New post   10 May 2021, 21:47
tomomnomnom wrote:
Archit3110
Hi Archit, I interpreted "between 50 and 150" as 50<area LMN<150. Thus, III, leading to an area of 150 exactly, would not be in the range. If, however, the correct translation would have been 50≤area LMN≤150, then the answer would indeed be E. Was my assumption wrong?




Hi, how did you come to the conclusion that 50 and 150 are not to be included? Do we have to assume such values to be excluded unless otherwise mentioned, for similar questions?
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Re: In right triangle LMN, the ratio of the longest side to the shortest [#permalink]
10 May 2021, 21:47
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