Question

A carpenter has three pieces of wood measuring 210 cm, 245 cm, 315 cm in length. She wants to cut the into shorter pieces that are all the same length, and width no wood left over. a. What is the greatest possible length of each shorter piece? b. How many shorter pieces will there be altogether?

Answer 1

The greatest possible length each shorter piece of wood can be cut into is 35 cm. By dividing each of the original lengths by 35 cm, we find there will be a total of 22 shorter pieces when no wood is left over.

Step-by-step explanation:

To find the greatest possible length for the shorter pieces of wood, we need to calculate the greatest common divisor (GCD) for the three lengths: 210 cm, 245 cm, and 315 cm. The GCD of these lengths is the largest number that divides into all of them without leaving a remainder. A good method to find the GCD is by using the Euclidean algorithm.

1. First, we find the GCD between 210 and 245, which is 35 cm.
2. Next, we find the GCD between 35 cm and 315 cm, which is also 35 cm.
3. Therefore, the greatest possible length for the shorter pieces is 35 cm.

To calculate the total number of shorter pieces:

• Divide 210 cm by 35 cm, which gives us 6 pieces.
• Divide 245 cm by 35 cm, resulting in 7 pieces.
• Divide 315 cm by 35 cm, giving us 9 pieces.

Adding them up, 6 + 7 + 9 we get a total of 22 shorter pieces.