HOT Competition 27 Aug/8PM: Triangle ABC has side lengths n, n+2, and

Question

Triangle ABC has side lengths n, n+2, and 3n-1, where n is an integer. What is the perimeter of Triangle ABC?

A. 11
B. 13
C. 16
D. 21
E. 23

Archit3110 · Accepted Answer

Triangle ABC has side lengths n, n+2, and 3n-1, where n is an integer. What is the perimeter of Triangle ABC?

A. 11
B. 13
C. 16
D. 21
E. 23 
 Perimeter of three sides as per given info is 5n+1 ; seeing answer options left with a,c,d ; 
also to note the third side ∆ property i.e sum of two sides > third side ; 
we see that only in option A ; 11 i.e n =2 we get sides 2,4,5 sufficient ; 
IMO A 11 is correct

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aviddd · Answer

Sides of triangle: n, n+ 2, 3n - 1. Add these to get perimeter = 5n + 1.

Out of answer choices, we can eliminate B and E, since they are not in the form of 5n + 1.

Remaining options: 11, 16, 21. In these cases, n will be 2, 3, 4.

n = 3. Sides: 3, 5, 8. Sum of 2 sides of triangle should be greater than third side. This condition is not met 3 +5 is not greater than 8. Invalid.

n = 4. Sides: 4, 6, 11. Sum of 2 sides of triangle should be greater than third side. This condition is not met 4+6 is not greater than 11. Invalid.

n = 2. Plugging into the sides, we get: 2, 4, 5. Meets the criteria of triangle. Correct.

Correct answer: A.

Saupayan · Answer

We know, for any triangle, the sum of any 2 sides is greater than the 3rd side.
=> n + (n+2) > 3n-1
=> 2n + 2 > 3n -1
=> n < 3
Since n is an integer (and n has to be positive), n = 1 or 2
if n = 1: the sides are 1, 3, 2 --> perimeter = 6
if n = 2: the sides are 2, 4, 5 --> perimeter = 11
Look at the options, 6 isn't there, 11 is the only possible choice

Answer : A

raunaqkapoor · Answer

taking examples
n=1
 n, n+2, and 3n-1 = 1,3,2

n=2
 n, n+2, and 3n-1 = 2,4,5
perimeter 11

n=3
n, n+2, and 3n-1 = 3,5,8
perimeter 16

n=4
n, n+2, and 3n-1 = 4,6,11
perimeter 21

in the last 2 the sum of 2 sides is not greater than the 3rd side hence they cannot be the ans as they donot make a triangle.

hence when n=2 perimeter is 11 which is the answer

ans: A

Posted from my mobile device

Crytiocanalyst · Answer

Employing the rule sum of 2 side should be greater than 3 rd side

From firat 2 sides we get n<3 , n=1,2

From 2nd and 3rd side in the rule we get n>1 , n=2

Therefore the perimeter =5*2 +1

Therefore IMO A

bumpbot · Answer

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HOT Competition 27 Aug/8PM: Triangle ABC has side lengths n, n+2, and

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