To solve this problem, follow these steps:
1. Understand the given ratio: The ribbon is divided in a ratio of 3:2. This means that for every 3 parts of the longer piece, there are 2 parts of the shorter piece.
2. Identify the length of the shorter piece: The length of the shorter piece of the ribbon is given as 6.4 cm.
3. Determine the total number of parts in the ratio: The ratio 3:2 consists of a total of [tex]\(3 + 2 = 5\)[/tex] parts.
4. Calculate the length of one part: Since the 6.4 cm corresponds to the 2 parts (shorter piece), we can find the length of one part by dividing the length of the shorter piece by the number of parts it represents.
[tex]\[
\text{Length of one part} = \frac{6.4 \text{ cm}}{2} = 3.2 \text{ cm}
\][/tex]
5. Find the length of the longer piece: The longer piece corresponds to 3 parts of the ratio. To find its length, multiply the length of one part by the number of parts in the longer piece.
[tex]\[
\text{Length of the longer piece} = 3 \times 3.2 \text{ cm} = 9.6 \text{ cm}
\][/tex]
So, the length of the longer piece is 9.6 cm.
