Final answer:
The length of the longer piece is 56 cm.
Step-by-step explanation:
To find the length of the longer piece, we need to determine the lengths of the two pieces of the ribbon using the given ratio. Let's call the lengths of the two pieces 4x and x. Since the ratio is 4:1, the total length of the ribbon is 4x + x = 5x. We can set up the equation 5x = 70 cm and solve for x. Dividing both sides of the equation by 5, we get x = 14 cm. Therefore, the length of the longer piece is 4x = 4 * 14 cm = 56 cm.