Question

Troy has a 45-inch piece of wire and a 63-inch piece of wire that he is cutting into smaller pieces. What is the longest each piece can be so that each piece is equally sized?

a) 9 inches

b) 15 inches

c) 18 inches

d) 21 inches

Answer 1

The longest equally sized pieces that can be cut from both a 45-inch and a 63-inch wire are 9 inches each, which is the greatest common divisor of the two lengths.

Step-by-step explanation:

To find the longest equally sized pieces Troy can cut from his 45-inch and 63-inch wires, we need to determine the greatest common divisor (GCD) of the two lengths, because each piece of wire must be an integer number of inches.

By listing the factors of 45 and 63, or using the Euclidean algorithm, we find that the GCD is 9 inches. This means the longest pieces Troy can cut from both wires where they are all equally sized is 9 inches.

Therefore, the correct answer is: a) 9 inches.