Grades 3-4 Video Solutions 2012-2012_3-4

Video Transcription

Problem number 23. A rectangular paper sheet measures 192 by 84 millimeters.  You cut the sheet along just one straight line to get two parts, one of which is a square.  Then you do the same with the non-square part of the sheet, and so on. What is the length of the  side of the small square you can get in this way? 1 millimeter, 4 millimeters, 6 millimeters, 10 millimeters, or 12 millimeters. So first, here is the rectangle.  So we need to start by dividing it, so we have this piece that's 84 by 84, and then we can do  that again, because 192 minus 84 is 108. So there's room for another 84. And then you see  that we have this small strip, and that is 24 by 84. You can cut this strip up into three squares  that are 24 by 24. And then you see we have this even smaller strip here, which is 12 millimeters  wide. Because this strip is 24 by 12, we can cut it in half again to make two 12 by 12 millimeter squares. And that is the small square we can get, which means our answer is E.

Video Summary

The problem involves cutting a rectangular sheet of dimensions 192 by 84 millimeters into squares through a series of cuts. Initially, an 84 by 84 millimeter square is cut, leaving a remaining 108 by 84 millimeter rectangle. Another 84 by 84 square is then cut from this, leaving a 24 by 84 millimeter strip. This strip can be divided into three 24 by 24 squares. Finally, the leftover strip of 24 by 12 millimeters can be halved into two 12 by 12 millimeter squares. Therefore, the smallest square achievable is 12 millimeters, corresponding to option E.

Keywords

rectangular sheet

square cuts

dimensions

smallest square

millimeters