Hints and solutions to
Make a List #2
A rectangle has an area of 120 sq. cm.. Its length and width are whole
numbers.
- What are the possibilities for the two numbers?
- Which possibility
gives the smallest perimeter?
-
As for yesterday's problem, we'll make a systematic list
- starting from 1 x 120
- of all the possible
dimensions of the rectangle. To do this, we need to figure out which
numbers divide evenly into 120 (in other words, what are possible
whole-number factors of 120).
- We can list only those for which the length
is less than the width.
- Besides columns for length and width, we will also have a column
for the perimeter (which is two times the length plus two times the width,
2L + 2W), so we can answer the question about which rectangle has the
smallest perimeter.
LengthWidthPerimeter
1120242
260124
34086
43068
52458
62052
81546
101244
And this shows all the possibilities where the length is less than the
width. The smallest perimeter is 44 cm,
for the
10 x 12 cm rectangle.
A rectangle has an area of 120 sq. cm.. Its length and width are whole
numbers.
- What are the possibilities for the two numbers?
- Which possibility gives the smallest perimeter?
- As for yesterday's problem, we'll make a systematic list - starting from 1 x 120 - of all the possible dimensions of the rectangle. To do this, we need to figure out which numbers divide evenly into 120 (in other words, what are possible whole-number factors of 120).
- We can list only those for which the length is less than the width.
- Besides columns for length and width, we will also have a column
for the perimeter (which is two times the length plus two times the width,
2L + 2W), so we can answer the question about which rectangle has the
smallest perimeter.
Length
Width
Perimeter
1
120
242
2
60
124
3
40
86
4
30
68
5
24
58
6
20
52
8
15
46
10
12
44
And this shows all the possibilities where the length is less than the width. The smallest perimeter is 44 cm, for the 10 x 12 cm rectangle.