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

The triangle lengths are 5, 7.5, and 10. The perimeter is 22.5 cm

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