High School

Two ribbons of lengths 270 cm and 180 cm are to be cut into strips of equal length.

A. Find the longest possible length for each strip.
B. How many strips can be cut from the ribbons?

Answer :

Final answer:

The longest length that can be cut from the ribbons is 90 cm. From the ribbons of length 270 cm and 180 cm, you can cut 3 strips and 2 strips respectively.

Explanation:

Cutting Ribbons into Equal Lengths

When cutting ribbons into equal lengths, we need to find the greatest common divisor (GCD) of the ribbon lengths. The GCD represents the longest length that can be cut from both ribbons without any remainder.

Finding the GCD

To find the GCD, we can use the Euclidean algorithm. Let's apply the algorithm to the given ribbon lengths:

  2. 270 ÷ 180 = 1 remainder 90
  4. 180 ÷ 90 = 2 remainder 0

The last non-zero remainder is 90, so the GCD of 270 and 180 is 90.

Longest Length

The longest length that can be cut from both ribbons is 90 cm.

Number of Strips

To find the number of strips that can be cut from each ribbon, we divide the ribbon length by the GCD:

  • 270 cm ÷ 90 cm = 3 strips
  • 180 cm ÷ 90 cm = 2 strips

Therefore, from the ribbons of length 270 cm and 180 cm, we can cut 3 strips and 2 strips respectively.

Learn more about cutting ribbons into equal lengths here:

https://brainly.com/question/246710

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