The length of the sides of a triangle are in the extended ration 3 : 10 : 12. the perimeter is 400 cm. what is the length of the longest side in centimeters

If the length of the sides of this triangle are in the extended ration:  3: 10:12; then we can express the length of its sides as: 3x ,10x and 12x.
The length of the longest side will be: 12x
Perimeter of a rectangle is the sum of all sides.
Therefore

We can suggest the following equation:

3x+10x+12x=400
25x=400
x=400/25
x=16

Therefore; the length of the sides would be:
3x=3(16)=48
10x=10(16)=160
12x=12(16)=192

the length of the longest side would be 192 cm. 

The sum is 2,160, no problem