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Bunuel
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In a triangle with integer side lengths, one side is three times as lo 26 Mar 2019, 05:40
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55% (hard)

Question Stats:

59% (02:01) correct 41% (01:58) wrong based on 150 sessions

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In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
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A
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In a triangle with integer side lengths, one side is three times as lo 26 Mar 2019, 06:03
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1 side =x
2 side = 3x
3 is 15 so, looking at the options if x = 8 perimeter is 47

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Lampard42
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In a triangle with integer side lengths, one side is three times as lo 26 Mar 2019, 07:49
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Difference between 2 sides must be lesser than 3 rd side. So assuming the longest side to be 24 then the third side 8 doesn’t work as difference is 24-15 =9. So 21 works as 21-15=6 while third side is 21/3 = 7. So the perimeter is 15+21+7= 43 option A.

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In a triangle with integer side lengths, one side is three times as lo 26 Mar 2019, 12:18
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Bunuel
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
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sides
x,3x,15
so 4x+15 perimeter
A. 4x=43-15 ; 28; x= 7 ; ok
B. 4x= 44-15 ; 29 , not ok fraction value of x
C ;4x= 45-15 ; 30 notok
d; 4x= 46-15 ; 31 again fraction
e; 4x= 47-15 ; 32 ok
negate all except A & E
now x= 8 , 7
if x=8 then value 8,32,15 ;
x=7; 7,21,15 ;
third property rule sum of two sides>third side
only possible at x= 7
so
IMO A sufficient
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In a triangle with integer side lengths, one side is three times as lo 26 Mar 2019, 15:08
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Bunuel
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
Show more

Any side of a Triangle has to be greater than the difference and less than the sum of the other two sides
so if the sides are X, 3x and 15 then:
2x<15<4x

To make the perimeter the largest x has to be 7.
Hence Perimeter 7 +21+15=43

Answer A
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In a triangle with integer side lengths, one side is three times as lo 26 Aug 2020, 19:39
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Let n = + Pos. Integer

the 3 Sides of the Triangle are then: 3n ; n ; and 15

Rule: the 2 Unknown Sides, when added, must have a SUM Greater Than > 15, the 3rd Side

3n + n > 15
4n > 15
N > 3.75

Since N must be an Integer the Minimum Value that N can take = 4

Rule: the DIFFERENCE between the 2 Unknown Sides must be LESS Than < 15, the 3rd Side

3n - n < 15
2n < 15
n < 7.5

Since N must be an Integer the Maximum Value that N can take = 7

Possible Values of N ---- [ 4 ; 5 ; 6 ; 7 ]

the Greatest Possible Perimeter of the Triangle will occur when N = 7

Then the Side = 3N = 21

and the 3rd Known Side = 15

7 + 21 + 15 = 43

Answer Choice A
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