Explanation

Since the sides are in the ratio 3:4:5, let's assume the common multiplier is x. Then, the sides can be written as 3x, 4x, and 5x.

The perimeter is the sum of all sides, so we can set up the equation:

3x + 4x + 5x = 24

Combine like terms:

12x = 24

Divide by 12:

x = 2

Now that we have the value of x, we can find the length of the longest side (5x):

5x = 5(2) = 10 cm

So, the length of the longest side is 10 cm.