Question

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?

Answer 1

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.

Answer 2

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

Answer 3

thank you