Chris in VA Posted June 2, 2011 Share Posted June 2, 2011 I don't have the actual problem in front of me, but it goes something like this-- Donna buys 28 linear feet of fencing. She wants to enclose the maximum amt of area. What dimensions should she use to enclose a space? She can make a rectangle or a square--which gives more space? So, other than guess and check, how can my dd solve this systematically? She doesn't know algebra yet. Quote Link to comment Share on other sites More sharing options...
nmoira Posted June 2, 2011 Share Posted June 2, 2011 Length plus width must equal 14 (i.e. half the perimeter). A chart is your best bet. Quote Link to comment Share on other sites More sharing options...
jennynd Posted June 2, 2011 Share Posted June 2, 2011 square give u largest area Quote Link to comment Share on other sites More sharing options...
Dana Posted June 2, 2011 Share Posted June 2, 2011 So, other than guess and check, how can my dd solve this systematically? She doesn't know algebra yet. For maximizing, you really want calculus. At this level, the problems are designed to be solved with guess & check (and a table is the best way to organize the information). The idea with the problem is to get the kids to recognize that a square does maximize area and to start seeing these problems before calculus :) Quote Link to comment Share on other sites More sharing options...
veggiegal Posted June 3, 2011 Share Posted June 3, 2011 You could use guess and check with the 28 ft, but to take it further you could use other set amounts of fencing (perimeter)--say, 12, 20, and 24 ft--and prove (making diagrams and a chart) that the largest area with least fencing is always a square rather than a rectangle. In fact, the largest area of all would be a circle, and a square comes "closer" to being a circle than a rectangle does (I hope you and your child can see than intuitively). Quote Link to comment Share on other sites More sharing options...
czny Posted June 3, 2011 Share Posted June 3, 2011 Make a table (or chart). Since width+length=14, you can list as follows 1*13=13 2*12=24 ... 6*8=48 7*7=49 <--- largest area Quote Link to comment Share on other sites More sharing options...
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