Brenda has two pieces of string, one 28 feet long and the other 42 feet long. For an art project, she wants to cut them up to produce many pieces of string that are all of the same length, with no string left over. What is the greatest length, in feet, that she can make them?

7 feet

Step-by-step explanation:

Length of one piece of string = 28 feet.

Length of the second string = 42 feet.

Since the number of required pieces was not given but many are required, the greatest length can be determined by;

If the maximum length is 7 feet, then:

the number of pieces from 28 feet long string =

                                                      = 4

Also,

the number of pieces from the 42 feet lone string =

                                                    = 6

Total number of 7 feet strings that she can make = 4 + 6

                                                    = 10

Since many pieces are required, the greatest length she can make is 7 feet. If she increase the length to 14 feet, the number of pieces would be 5 which limit the required number.