1. The document determines the maximum dimensions of a corn farm that a farmer can fence using 100 meters of wire. The largest area is 625 square meters which occurs when the length and width are both 25 meters, making the field a square. 2. Using recommended spacing of corn seedlings, the document calculates the farmer can plant 4592 seedlings in the 625 square meter field by planting them in 28 rows with 164 seedlings in each row. 3. The calculations allow the farmer to utilize the maximum space available and determine the optimal number of seedlings to plant.

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MATHEMATICS SCHOOL BASED ASSESMENT
DETERMINING THE DIMENSIONS OF A CORN
FARM TO GIVE MAXIMUM USE OF SPACE

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TABLE OF CONTENTS
TITLE PAGE
Acknowledgement………………………………………………………………………………………...3
Title of Project……………………………………………………………………………………………….4
Purpose of Project…………………………………………………………………………………………4
Problem Statement …….………………………………………………………………………………..5
Problem Formulation …………………..……………………………………………………………….6
Data Analysis ……………..…………………………………………………………………………………7
Problem Calculation and Analysis …….…………………………………………………………..8
Discussion of Findings .…………….……………………………..…………………………………….9
Conclusion …………………………….………………………………………………………………………9
Bibliography …………………………………………………………………………………………………10

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ACKNOWLEDGEMENT
I would like to express my special thanks to all the persons who helped me with
this project.
Thank you all for your continuous help and support.

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TITLE OF PROJECT
Determining the maximum dimensions of a corn farm and the number of seedlings
that can be planted on it.
INTRODUCTION
PURPOSE OF STUDY
The purpose of the project is to determine the dimensions that will give maximum
space for the amount of wire that a farmer has available.
My neighbor, Farmer Joe was given two rolls of wire by the Rural Agricultural
Development Authority (RADA) Foundation. This is in aid of helping him to put
up a fencing for the corn he wanted to invest in. Each roll of wire is 50 metres
long. Mr. Joe has sought my assistance with the calculations for the maximum
space that he can enclose with his 100 metres of wire and the number of corn
seedlings that he can plant. He wants a rectangular farm for his corn, and he wants
to utilize as much space as possible.
Problem Solution
1 roll of wire = 50 metre
2 rolls of wire = 2 x 50 = 100 m
Mr. Joe has 100 metres of wire available.

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The perimeter of wire that the farmer has amounts to 100 metres. Efforts were
made to get the dimensions that would give a rectangle so that the largest area can
be found. It was decided to start with the smallest unit of one on both widths of a
rectangle as shown.
The table was constructed starting with the width of 1m, then doing the
calculations to get the length.
Width Length Area
1 m 100 – (1 + 1) = 98, 48 ÷ 2 = 49 49 49 x 1 = 49
2 m 100 – (2 + 2) = 96, 96 ÷ 2 = 48 48 48 x 2 = 99
1m
24m
24m
1m

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Problem Calculation
Perimeter = 100 metres
Width Calculations Length Area
1 m 100 – (1 + 1) = 98, 98 ÷ 2 = 49 49 49 x 1 = 49
2 m 100 – (2 + 2) = 96, 96 ÷ 2 = 48 48 48 x 2 = 99
3 m 100 – (3 + 3) = 94, 94 ÷ 2 = 47 47 47 x 3 = 141
4 m 100 – (4 + 4) = 92, 92 ÷ 2 = 46 46 46 x 4 = 184
5 m 100 – (5 + 5) = 90, 90 ÷ 2 = 45 45 45 x 5 = 225
6 m 100 – (6 + 6) = 88, 88 ÷ 2 = 44 44 44 x 6 = 264
7 m 100 – (7 + 7) = 86, 86 ÷ 2 = 43 43 43 x 7 = 301
8 m 100 – (8 + 8) = 84, 84 ÷ 2 = 42 42 42 x 8 = 336
9 m 100 – (9 + 9) = 82, 82 ÷ 2 = 41 41 41 x 9 = 369
10 m 100 – (10 + 10) = 80, 80 ÷ 2 = 40 40 40 x 10 = 400
11 m 100 – (11 + 11) = 78, 78 ÷ 2 = 39 39 39 x 11 = 429
12 m 100 – (12 + 12) = 76, 76 ÷ 2 = 38 38 38 x 12 = 456
13 m 100 – (13 + 13) = 74, 74 ÷ 2 = 37 37 37 x 13 = 481
14 m 100 – (14 + 14) = 72, 72 ÷ 2 = 36 36 36 x 14 = 504
15 m 100 – (15 + 15) = 70, 70 ÷ 2 = 35 35 35 x 15 = 525
16 m 100 – (16 + 16) = 68, 68 ÷ 2 = 34 34 34 x 16 = 544
17 m 100 – (17 + 17) = 66, 66 ÷ 2 = 33 33 33 x 17 = 561
18 m 100 – (18 + 18) = 64, 64 ÷ 2 = 32 32 32 x 18 = 576
19 m 100 – (19 + 19) = 62, 62 ÷ 2 = 31 31 31 x 19 = 589
20 m 100 – (20 + 20) = 60, 60 ÷ 2 = 30 30 30 x 20 = 600
21 m 100 – (21 + 21) = 58, 58 ÷ 2 = 29 29 29 x 21 = 609
22 m 100 – (22 + 22) = 56, 56 ÷ 2 = 28 28 28 x 22 = 616
23 m 100 – (23 + 23) = 54, 54 ÷ 2 = 27 27 27 x 23 = 621
24 m 100 – (24 + 24) = 52, 52 ÷ 2 = 26 26 26 x 24 = 624
25 m 100 – (25 + 25) = 50, 50 ÷ 𝟐 = 25 25 25 x 25 = 625
26 m 100 – (26 + 26) = 48, 48 ÷ 2 = 24 24 24 x 26 = 624
27 m 100 – (27 + 27) = 46, 46 ÷ 2 = 23 23 23 x 27 = 621
28 m 100 – (28 + 28) = 44, 44 ÷ 2 = 22 22 22 x 28 = 616

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The lengths and the widths were then used to find the area, and the highest value
observed.
DATA ANALYSIS
The calculations above have shown that the largest area that can be enclosed with
the 100 metres of wire will be 625m2
. This was had when the length of the
rectangle is 10 m and width is 10 m. With the length and the width being equal,
the polygon is a square. Since the square is a rectangle, Mr. Joe will have his
rectangular corn field.
After the land is fenced with the largest possible area, the seedlings will be ready
for planting.
According to research, corn loves hot climate like Jamaica/Belize. It is said that the
corns that grow in temperature greater than 65o
C are the sweetest. To get the best
crop of corn, experts say the seeds should be planted 1 inch deep and 4 to 6 inches
25 m
25 m

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apart. Rows should be 30 to 36 inches apart. Retrieved from:
http://www.almanac.com/plant/corn. This will be used to guide the calculation for
the number of seedlings Mr. Joe will invest in.
Problem Calculation and Analysis
With that specification, I will calculate the number of seedlings to plant in the
625m2
of land.
25 m = 984.25 inches; rounded to nearest whole number gives:
25 m = 984 inches
Rows should be 30 to 36 inches apart according to the experts. Using 35 inches
apart will give: 984. ÷ 35 = 28.1
It is therefore recommended that Mr. Joe has 28 rows, each being approximately
35 inches apart.
Seedlings should be 4 to 6 inches apart, so using 6 inches gives length of row
divide by 6.
984. ÷ 6 = 164
Each row has 164 seedlings.
28 rows x 164 = 4592 seedlings.
984 in
984 in

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Mr. Joe has space to plant 4592 seedlings on the plot of land that he has fenced.
Rows should be 30 to 36 inches apart, and seedlings 4 to 6 inches apart in each
row. If Farmer Joe follows the specification, the rows should be similar to the
diagram above.
DISCUSSION OF FINDINGS
Finding the maximum area from a given perimeter can be done by writing out the
lengths and the widths and taking their products. One may think that the large
lengths would give the maximum area but this was not so. It works out that when
the length and the width were equal, that is when the largest area occurred.
In determining the number of seedlings, one must first ensure that the values being
compared are of the same unit. The length was then divided to get the number of
rows, and the length of a row divided to get the number of seedlings in each row.
The total number of seedlings was derived by multiplying the number of rows by
the number in each row. This calculation will assist the farmer in making the
proper choice to get a good crop of corn.
CONCLUSION
The maximum area that can be had from a perimeter of 100m is 625m2
. This
occurred from the length and the width being equal.

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The total number of seedlings to be planted on this plot of land, based on the
recommended spacing of experts, is 4592.

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BIBLIOGRAPHY
Sweet Corn: Planting, Growing and Harvesting Sweet Corn. Retrieved from
http://www.almanac.com/plant/corn
Toolsie, R. (1996). Mathematics: A Complete Course with C.X.C. Questions, San
Fernando: Caribbean Educational Publishers.