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2 sides in both the triangles ABC and DEF are 5 and 10 respectively.
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Updated on: 15 Jan 2022, 17:11
Updated on: 15 Jan 2022, 17:11
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2 sides in both the triangles ABC and DEF are 5 and 10 respectively.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The greatest possible integer difference between the parameters of two triangles |
9 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Originally posted by KarunMendiratta on 16 Feb 2021, 22:43.
Last edited by Carcass on 15 Jan 2022, 17:11, edited 2 times in total.
Last edited by Carcass on 15 Jan 2022, 17:11, edited 2 times in total.
Formatted
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: 2 sides in both the triangles ABC and DEF are 5 and 10 respectively.
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17 Feb 2021, 22:22
17 Feb 2021, 22:22
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OA Explanation
Perimeter of ABC = \(15 + x\)
Perimeter of DEF = \(15 + y\)
In a triangle, any side must be less than the sum of other 2 sides and at the same time, greater than the positive difference between them.
\(10 - 5 < x < 10 + 5\)
\(5 < x < 15\)
\(10 - 5 < y < 10 + 5\)
\(5 < y < 15\)
Let us assume that Perimeter or ABC > Perimeter of DEF
So, Maximum possible integer difference = \( x - y\)
Therefore, we must put maximum value for \(x\) and least value for \(y\)
NOTE: The difference of Perimeters must be an integer, that doesn't mean the sides must be an integer value too!
To get an integer value, Maximum value of \(x = 14.5\) and Minimum value of \(y = 5.5\)
i.e. \(14.5 - 5.5 = 9\)
Col. A = Col. B
Hence, option C
Perimeter of ABC = \(15 + x\)
Perimeter of DEF = \(15 + y\)
In a triangle, any side must be less than the sum of other 2 sides and at the same time, greater than the positive difference between them.
\(10 - 5 < x < 10 + 5\)
\(5 < x < 15\)
\(10 - 5 < y < 10 + 5\)
\(5 < y < 15\)
Let us assume that Perimeter or ABC > Perimeter of DEF
So, Maximum possible integer difference = \( x - y\)
Therefore, we must put maximum value for \(x\) and least value for \(y\)
NOTE: The difference of Perimeters must be an integer, that doesn't mean the sides must be an integer value too!
To get an integer value, Maximum value of \(x = 14.5\) and Minimum value of \(y = 5.5\)
i.e. \(14.5 - 5.5 = 9\)
Col. A = Col. B
Hence, option C
General Discussion
Re: 2 sides in both the triangles ABC and DEF are 5 and 10 respectively.
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17 Feb 2021, 20:30
17 Feb 2021, 20:30
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Least perimeter = 5 + 6 + 10 = 21
Greatest perimeter = 5+ 10 + 14 = 29
So shouldn't answer be B ?
KarunMendiratta What am I missing?
Greatest perimeter = 5+ 10 + 14 = 29
So shouldn't answer be B ?
KarunMendiratta What am I missing?
