# Pow 10: Possible Patches

**Topics:**Rectangle

**Pages:**2 (604 words)

**Published:**September 17, 2009

Problem Statement:

The story in this POW goes that there is a girl named Keisha that is making a patchwork quilt, it will be made of rectangular patches. Keisha finds a piece of satin that’s dimensions are 17in by 22in. Our goal is to try to get the most from the piece of satin, in other words try to get as many rectangular shapes from her piece of satin. The rectangular shapes have to be 3in by 5in. Check out http://minorleaguegamer.com

Process:

The methods used on this problem: In this problem I took both a geometrical and mathematical approach to the problem. My first method was to divide up each side so that I could get as much rectangles on each side, for example for the side with 22in I would type this in to my calculator: (22 – 5 – 5 – 3 – 3 – 3 – 3 = 0) I did not find this out at first, it took a while till I got the correct amounts of “3s” and “5s” to subtract from the “22” that would equal “0” because I wanted to be efficient and fill up as much as a I could in that line. I did the same thing for the side with 17in. However I noticed that when I moved on to the next question in the POW it asked me to try different sized rectangular shapes, that’s is when I noticed that I could not make it equal “0” so I just settle for the smallest number I could get. The second method I used to try to figure out this POW was to; after I filled the sides with shapes, fill in the middle by, just like in the first method, dividing the remaining spaces and trying to get the most out of the remaining space. The third method was a way of checking that there was no more pieces I could use, what I did was I counted how much spaces where left, then counted how many spaces it took to fill up the rectangle. If the amount of spaces left exceeded the amount it took to fill the rectangle I would double-check to make sure there wasn’t another I could put in there by rearranging the shapes in a different way. However with other sized shapes...

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