The sides of a triangle are in the ratio 2: 3: 4. the shortest side has length 5cm. find the perimeter

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