Can you help me solve this math problem?

[Chris in VA]

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.

[nmoira]

Length plus width must equal 14 (i.e. half the perimeter). A chart is your best bet.

[jennynd]

square give u largest area

[Dana]

 

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 :)

[veggiegal]

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).

[czny]

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