The Department of Mathematics Education. EMAT 6700 J. Wilson

The goal of the problem is to maximize the area. In order to accomplish this, we first need to look at how the area is formed based on the dimensions. Assuming the garden is rectangular, area = length x width. We can use a spreadsheet to calculate all possible dimensions for a rectangle that has a perimeter equal to 100 meters.

Length Width Area
1 49 49
2 48 96
3 47 141
4 46 184
5 45 225
6 44 264
7 43 301
8 42 336
9 41 369
10 40 400
11 39 429
12 38 456
13 37 481
14 36 504
15 35 525
16 34 544
17 33 561
18 32 576
19 31 589
20 30 600
21 29 609
22 28 616
23 27 621
24 26 624
25 25 625
26 24 624
27 23 621
28 22 616
29 21 609
30 20 600
31 19 589
32 18 576
33 17 561
34 16 544
35 15 525
36 14 504
37 13 481
38 12 456
39 11 429
40 10 400
41 9 369
42 8 336
43 7 301
44 6 264
45 5 225
46 4 184
47 3 141
48 2 96
49 1 49

When the data above is graphed, it gives us a quadratic equation. Does this make sense? Why is this so? Could you write an expression that models the function below? How is the maximum area modeled in the function?

Click Here to view Excel file.

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