Solve the following:
Farmer Lee wants to make a fence for his chicken coop in the shape of
a rectangle. He has 20 meters of fence. Construct some of the sizes of
rectangles that he could make as
• Same area but different perimeters
• Which shape would be best for the farmer? Justify your answer.
Answers
Answer:
Calculate the area of a number of rectangles and then choose the dimensions that give the largest area.
ChickenRun.gif (1537 bytes)
For example: If Henry's chicken run has these dimensions the area is 1 x 5 = 5 square metres.
If Henry's chicken run is 2 x 4 metres, the area is 8 square metres.
If the side lengths are all 3 metres, the area is 3 x 3 = 9 square metres.
Hence the maximum area is 9 square metres.
Second part of problem:
Henry must do considerably more calculations. A table is the clearest way to show these.
width
length
area
(metres)
(metres)
(square metres)
1
29
29
2
28
56
3
27
81
4
26
104
5
25
125
6
24
144
7
23
161
8
22
176
9
21
189
10
20
200
11
19
209
12
18
216
13
17
221
14
16
224
15
15
225
From the table we see that Henry’s largest chicken run has area 225 square metres.