The sides are in ratio 2:3:4
So this means
shortest side = 2x
medium side = 3x
longest side = 4x
for some number x
The shortest side is given to be 5 cm, meaning that
2x = 5
x = 5/2 <--- divide both sides by 2
x = 2.5
Since x = 2.5, we can now say...
shortest side = 2*x = 2*2.5 = 5
medium side = 3*x = 3*2.5 = 7.5
longest side = 4*x = 4*2.5 = 10
The three sides of the triangle are: 5, 7.5, 10
They add to 5+7.5+10 = 22.5
The perimeter of this triangle is 22.5 centimeters