A segment 12" long is divided into two segments having lengths in the ratio of 2:3. Find the length of each segment. (Hint: Let 2x and 3x represent the length of the parts.)

x = ?

segment 1 = (2x) = ? inches
segment 2 = (3x) = ? inches

similar to the other one

To find the lengths of the two segments, we'll set up an equation based on the given information.

Let's assume that the length of the shorter segment (2x) is represented by 2x, and the length of the longer segment (3x) is represented by 3x. Since the given ratio is 2:3, the total length of the segments must add up to 12 inches.

So, we can write the equation as:

2x + 3x = 12

Combining like terms, we have:

5x = 12

Now, to solve for x, we divide both sides of the equation by 5:

x = 12 / 5

Therefore, x is equal to 2.4.

To find the lengths of the segments, we substitute the value of x back into our expressions for the two segments:

Segment 1 = 2x = 2 * 2.4 = 4.8 inches

Segment 2 = 3x = 3 * 2.4 = 7.2 inches

Therefore, the length of the two segments are:

Segment 1 = 4.8 inches
Segment 2 = 7.2 inches