If the sides of a triangle are in the ratio 5: 12: 13, what is the length of each side of the triangle if the perimiter of the triangle is 15

So the perimeter of the first triangle is 30; since you are given each side you can set up 3 ratios to find the unknown side lengths.
Thus side 5 would correspond to 2.5
Side 12 would correspond to 6
And side 13 would be 6.5

Another way to look at it is that since the perimeter of triangle 2 decreases by half (from 30 to 15), you can assume all side will also decrease by half

5x+12x+13x=15
30x=15
x=15:30
x=0,5
5*0,5=2,5
12*0.5=6
13:0,5=6,5

2,5+6+6,5=15