a 33 long rod is to be divided into three parts, each of which is progressively longer than the next part by 2 cm. how long is each part?

solution pls.

L + L+2 + L+4 = 33

what is L?

9,11,13

To solve this problem, let's start by representing the lengths of the three parts.

Let's assume the first part's length is x cm.
According to the problem, the next part is longer than the first part by 2 cm. Therefore, the second part's length would be (x + 2) cm.
Similarly, the third part is longer than the second part by 2 cm. So, the third part's length would be (x + 2 + 2) cm, which simplifies to (x + 4) cm.

Now, we know that the sum of the lengths of these three parts is equal to the length of the entire rod, which is 33 cm. Therefore, we can set up the equation:

x + (x + 2) + (x + 4) = 33

Simplifying the equation:

3x + 6 = 33
3x = 27
x = 9

Now that we have determined the length of the first part (x = 9 cm), we can calculate the lengths of the other parts:

First part: x cm = 9 cm
Second part: (x + 2) cm = (9 + 2) cm = 11 cm
Third part: (x + 4) cm = (9 + 4) cm = 13 cm

Therefore, each part is 9 cm, 11 cm, and 13 cm long, respectively.