Posted by **itrixie** on Friday, August 15, 2014 at 5:28pm.

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?

- Geometry -
**Henry**, Friday, August 15, 2014 at 5:59pm
One side = L units.

2nd side = 3L units.

3rd side = 15 units.

3L < 15

L < 5

L = 4 = Largest possible integer.

3L = 3*4 = 12.

P = 4 + 12 + 15 = 31 = Max. possible

perimeter.

- Geometry -
**Steve**, Friday, August 15, 2014 at 11:37pm
for sides a<b<c

c-b < a < c+b

So, if 3L is the longest side

15-L < 3L < L+15

15 < 4L < 2L+15

L > 3.75

L < 7.5

So, the extreme is 7,15,21 for a perimeter of 43

- Geometry -
**itrixie**, Saturday, August 16, 2014 at 4:05pm
thank you

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