MathDB
rectangular sheets

Source: 1961-62 Germany R4 12.3 https://artofproblemsolving.com/community/c3208025_

October 12, 2024
geometry

Problem Statement

With a roller shear, rectangular sheets of 14201420 mm wide should be made, namely with a width of 500500 mm and a total length of 10001000 m as well as a width of 300300 mm and a total length of 18001800 m can be cut. So far it has been based on the attached drawing cut, in which the gray area represents the waste, which is quite large. A socialist brigade proposes cutting in such a way that waste is significantly reduced becomes. a) What percentage is the waste if cutting continues as before? b) How does the brigade have to cut so that the waste is as small as possible and what is the total length of the starting sheets is required in this case? c) What percentage is the waste now? https://cdn.artofproblemsolving.com/attachments/f/8/c6c88b79abb5d34674bf54524ae1731985c3f7.png