1 mMaximum Areas.....Click Here to Download File
The Swimming Area Problem : Grade 7 Version
You have a summer job as a lifeguard at the waterfront. Your boss gives you 100 m of rope and tells you to enclose a rectangular swimming area that surrounds a floating platform. You decide that you want to enclose as large an area as possible for the swimmers.
Problem: What dimensions will make the greatest swimming area?
Recall the formulas for Perimeter and Area
P = 2l + 2w A = lw
Hypothesis: Make a hypothesis about the dimensions of the shape that will give the largest swimming area given 100 m of rope.
Data Collection: Calculate the perimeter and area of different possible rectangles.
1 a) Consider the following swimming area:
49 m
1 m
i)
Calculate the perimeter of the swimming area.
ii) Calculate the area of the swimming area.
b) Consider the following swimming area:
30 m
20 m
i) Calculate the perimeter of
the swimming area.
ii) Calculate the area of the swimming area.
2. Complete this chart to determine the areas for other possible rectangular shapes with perimeter of 100 m.
|
Perimeter (m) |
Length (m) |
Width (m) |
Area (m2) |
|
100
|
50 |
|
|
|
100
|
49 |
1 |
49 |
|
100
|
30 |
20 |
|
|
|
45 |
|
|
|
|
40 |
|
|
|
|
35 |
|
|
|
|
25
|
|
|
|
|
20 |
|
|
|
|
15 |
|
|
|
|
10 |
|
|
|
|
5 |
|
|
|
|
1 |
|
|
|
|
0 |
|
|
Did you need to complete the whole chart? Explain your answer.
3. Construct a line graph using the data from the table in Question #2 Use length and area as your axis. Length is on the horizontal axis and area is on the vertical axis. Be sure that the graph includes a title and that the axes are labeled.
Conclusion:
4. Consider the data from the table and your graph.
a)
What dimensions would give the largest swimming area?
b) Draw a diagram of the maximum swimming area and label it.
5.
Was your hypothesis correct? Make any necessary changes.
6. If you were given 160 m of rope, what dimensions would give the maximum area? Draw a diagram and label it.
EXTENSION ACTIVITY:
Now you want to use the same length of rope to enclose a swimming area that uses the beach as one of the sides. What dimensions would now give the maximum swimming area?