GCSE Maths Coursework: Strand 1 - Making and monitoring decisions
Equable shapes:
The task set is to investigate equable rectangles and further shapes. An equable shape is a shape whose perimeter is 'numerically equal to its area'.
Equable Rectangles
To start off my investigation I decided to experiment by drawing several rectangles with random lengths and widths. My drawings are included on graph paper. (see page )
I then decided using a table I would investigate every rectangle between that had a width or length between one and ten (whole numbers only). I worked out each shapes area and perimeter and if they were equal I highlighted them:
Length
Base
Area
Perimeter
4
2
2
6
3
3
8
4
4
0
5
5
2
6
6
4
7
7
6
8
8
8
9
9
20
0
0
22
2
2
6
2
2
4
8
2
3
6
0
2
4
8
2
2
5
0
4
2
6
2
6
2
7
4
8
2
8
6
20
2
9
8
22
2
0
20
24
3
3
8
3
2
6
0
3
3
9
2
3
4
2
4
3
5
5
6
3
6
8
8
3
7
21
20
3
8
24
22
3
9
27
24
3
0
30
26
4
4
0
4
2
8
2
4
3
2
4
4
4
6
6
4
5
20
8
4
6
24
20
4
7
28
22
4
8
32
24
4
9
36
26
4
0
40
28
5
5
2
5
2
0
4
5
3
5
6
5
4
20
8
5
5
25
20
5
6
30
22
5
7
35
24
5
8
40
26
5
9
45
28
5
0
50
30
6
6
4
6
2
2
6
6
3
8
8
6
4
24
20
6
5
30
22
6
6
36
24
6
7
42
26
6
8
48
28
6
9
54
30
6
0
60
32
7
7
6
7
2
4
8
7
3
21
20
7
4
28
22
7
5
35
24
7
6
42
26
7
7
49
28
7
8
56
30
7
9
63
32
7
0
70
34
8
8
8
8
2
6
Equable shapes:
The task set is to investigate equable rectangles and further shapes. An equable shape is a shape whose perimeter is 'numerically equal to its area'.
Equable Rectangles
To start off my investigation I decided to experiment by drawing several rectangles with random lengths and widths. My drawings are included on graph paper. (see page )
I then decided using a table I would investigate every rectangle between that had a width or length between one and ten (whole numbers only). I worked out each shapes area and perimeter and if they were equal I highlighted them:
Length
Base
Area
Perimeter
4
2
2
6
3
3
8
4
4
0
5
5
2
6
6
4
7
7
6
8
8
8
9
9
20
0
0
22
2
2
6
2
2
4
8
2
3
6
0
2
4
8
2
2
5
0
4
2
6
2
6
2
7
4
8
2
8
6
20
2
9
8
22
2
0
20
24
3
3
8
3
2
6
0
3
3
9
2
3
4
2
4
3
5
5
6
3
6
8
8
3
7
21
20
3
8
24
22
3
9
27
24
3
0
30
26
4
4
0
4
2
8
2
4
3
2
4
4
4
6
6
4
5
20
8
4
6
24
20
4
7
28
22
4
8
32
24
4
9
36
26
4
0
40
28
5
5
2
5
2
0
4
5
3
5
6
5
4
20
8
5
5
25
20
5
6
30
22
5
7
35
24
5
8
40
26
5
9
45
28
5
0
50
30
6
6
4
6
2
2
6
6
3
8
8
6
4
24
20
6
5
30
22
6
6
36
24
6
7
42
26
6
8
48
28
6
9
54
30
6
0
60
32
7
7
6
7
2
4
8
7
3
21
20
7
4
28
22
7
5
35
24
7
6
42
26
7
7
49
28
7
8
56
30
7
9
63
32
7
0
70
34
8
8
8
8
2
6