Transcript Optimum Area and Perimeter

Optimum Area and Perimeter
Second Attempt at Lesson
Note – All Four Sides
• The maximum area for a rectangular
shape for a given perimeter is a square.
• The minimum perimeter for a rectangular
shape for a given area is a square.
**For any shape, the maximum area for a
given perimeter would be a circle!!
Examples
• Find the dimensions and the optimal value
for the following:
– A rectangular shape with a 110m perimeter
– A rectangular shape with an area of 110m2
Notes – Only Three Sides
• The maximum area and minimum
perimeter occur when the length (side
parallel to the side without the border) is
twice the width.
l = 2w
Example
The City of Ottawa wants to fence off a
swimming area at Moonie’s Bay Beach. Find
the optimal value given the information below.
a. The maximum swimming area that can be
enclosed with 220m of rope.
b. The minimum rope needed to enclose a
3200m2 swimming area.
Example - Max Area
Perimeter (m)
Width (m)
Length (m)
Area (m2)
220
5
10
20
30
210
200
180
160
1050
2000
3600
4800
40
50
60
140
120
100
5600
6000
6000
55
110
6050
Example – Min. Perimeter
Area (m2)
Width (m)
Length (m)
Perimeter (m)
3200
10
20
30
40
320
160
106.7
80
340
200
166.7
160
50
35
45
64
91.4
71.1
164
161.4
161.1
confirm
Other Number of Sides
• Investigate … use a table!!
• Columns:
– Perimeter
– Length
– Width
– Area
Example
Farmer Joe has 200m of fencing and he wants
to create the following pens for his animals
(pigs, chickens and goats). Find the maximum
area he can enclose.
Example
Farmer Joe has decided he needs to give his
animals 1200m2 of area. Find the minimum
amount of fencing he needs to purchase.
Homework
• Retry … OR Do the First Time … 
– The Garden Fence (from Handout)
– Pg. 433 # 11
• Two Problems (on this handout)
– Daddy Day Care
– Miss. Nieuwenhuis’ Garden
Garden Fence
Perimeter (m)
120
Width (m)
2
4
5
10
15
20
25
Length (m)
57
54
52.5
45
37.5
30
22.5
Area (m2)
114
216
262.5
450
562.5
600
562.5
Pg. 433 # 11
Perimeter(m)
3600/6.25
Width (m)
Length (m)
Area (m2)
=576
10
20
40
60
268
248
208
168
2680
4960
8320
10080
70
80
65
148
128
158
10360
10240
10270
75
72
138
144
10350
10368
Daddy Day Care
Perimeter (ft)
Width (ft)
Length (ft)
Area (ft2)
250
10
230
2300
20
210
4200
30
190
5700
40
170
6800
50
150
7500
60
130
7800
70
110
7700
55
140
7700
65
120
7800
62.5
125
7812.50
62
126
7812
63
124
7812
confirm
Miss N’s Garden
Area (ft2)
Width (ft)
Length (ft)
Perimeter (ft)
80
2
4
8
40
20
10
126
72
54
10
9
8
8.9
54
53.7