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The lengths of three sides of a triangle are 12, 17, and x. The perime
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11 Mar 2021, 03:38
11 Mar 2021, 03:38
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The lengths of three sides of a triangle are 12, 17, and x. The perimeter of the triangle could be which of the following?
Indicate all that apply.
28
34
40
57
60
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Indicate all that apply.
28
34
40
57
60
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The lengths of three sides of a triangle are 12, 17, and x. The perime
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11 Mar 2021, 08:09
11 Mar 2021, 08:09
Carcass wrote:
The lengths of three sides of a triangle are 12, 17, and x. The perimeter of the triangle could be which of the following?
Indicate all that apply.
28
34
40
57
60
Indicate all that apply.
28
34
40
57
60
Any side in a triangle must be less than the sum of other 2 sides and at the same time, must also be greater than the positive difference between them
\(|17 - 12| < x < 12 + 17\)
\(5 < x < 29\)
\(Perimeter (P) = 12 + 17 + x = 29 + x\)
Adding 29 into the inequality;
\(5 + 29 < x + 29 < 29 + 29\)
\(34 < P < 58\)
Hence, option C and D
The lengths of three sides of a triangle are 12, 17, and x. The perime
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29 Apr 2021, 18:12
29 Apr 2021, 18:12
Using that same principle, I approached a slightly different way to find the extremes without using inequalities.
Max x: 12+17 > x
Min x: 12+x > 17
Max x < 29
Min x > 5
But we are asked about the perimeter, so now that we know the ranges of x, we can find the min and max:
Max P = 17+12+29 = 58
Min P = 17+12+5 = 34
Now we have to be careful, because these are not inclusive numbers, so we have to look slightly inside this range.
C and D
Max x: 12+17 > x
Min x: 12+x > 17
Max x < 29
Min x > 5
But we are asked about the perimeter, so now that we know the ranges of x, we can find the min and max:
Max P = 17+12+29 = 58
Min P = 17+12+5 = 34
Now we have to be careful, because these are not inclusive numbers, so we have to look slightly inside this range.
C and D
