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• Level: GCSE
• Subject: Maths
• Word count: 1536

# Opposite corner

Extracts from this document...

Introduction

Opposite Corner

Candidate Sheet

Opposite corner

Firstly i will investigate the difference between the products of the numbers in oppsite corners of any rectangle that can be drawn in a 100-sqaure grid. After that i will choose randomly some rectangles from the 100-sqaure grids. After that i will mutiply the top right corner with bottom left corner (which will be coloured in blue) then i will multiply the bottom right corner with the top left corner (which will be coloured in yellow). After that i will find the answer then i will subtract the smallest number with biggest number, which will give me the answer of the opposite corner.

This is a diagram of a 100-sqaure grid.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

1) (A) From the 100 sqaure i will choose a rectangle sided 2 by 3 horizontally

 4 5 6 14 15 16

The products of the number in the opposite corner of this rectangle are:

4x16 = 64

14x6 = 84

The difference between these products is

84-64=20

The difference is 20

 8 9 10 18 19 20

The product of the number in the opposite corner of this rectangle is:

8x20=160

18x10=180

The differences between these products are:

160-180=20

Middle

5

6

7

14

15

16

17

The product of the number in the opposite corner of this rectangle is:

4x17=68

14x7=98

The difference between these products is:

68-98=30

The difference is 30

 24 25 26 27 34 35 36 37

The products of the number in the opposite corner of this rectangle are:

24x37=888

34x27=918

The differences between these products are:

888-918=30

The difference is 30

Now i have found out that a rectangle sized 2 by 4 is on anywhere in a 100 sqaure grid the difference is always going to be 30

I am going to choose a rectangle from the 100-sqaure grids sided 2 by 5 horizontally

 1 2 3 4 5 11 12 13 14 15

The products of the number in the opposite corner of this rectangle are:

1x15=15

11x5=55

The differences between these products are:

55-15=40

The difference is 40

 21 22 23 24 25 31 32 33 34 35

The products of the number in the opposite corner of this rectangle are:

21x35=735

31x25=775

The difference between these products is:

735-775=40

The difference is 40

 6 7 8 9 10 16 17 18 19 20

The products of the number in the opposite corner of this rectangle are:

6x20=120

16x10=160

The difference between these products is:

120-160=40

The difference is 40

Now i have found out that a rectangle sized 2 by 5 is on anywhere in a 100 sqaure grid it is always going to be 40

Now i am going to choose a rectangle from the 100-sqaure grids sided 2 by 6 horizontally

 25 26 27 28 29 30 35 36 37 38 39 40

The product of the number in the opposite corner of this rectangle is:

25x40=1000

35x30=1050

The difference between these products is:

1000-1050=50

The difference is 50

 85 86 87 88 89 90 95 96 97 98 99 100

The product of the number in the opposite corner of this rectangle is:

85x100=8500

95x90=8550

The difference between these products is:

8500-8550=50

The difference is 50

 62 63 64 65 66 67 72 73 74 75 76 77

The product of the number in the opposite corner of this rectangle is:

62x77=4774

72x67=4824

The difference between these products is:

4824-4774=50

The difference is 50

Now i have found out that a rectangle sized 2 by 6 is on anywhere in the 100 sqaure grid the difference will always going to be 50

Now i have found out that if i go up by 1 horizontally (e.g. 2 by 7, 2 by 8, 2 by 9...) the answer will go up by 10.

From the 100-sqaure grids I will now choose a rectangle 2 by 3 vertically

 1 2 11 12 21 22

The product of the number in the opposite corner of this rectangle is:

1x22=22

21x2=42

The difference of this product is:

42-22=20

The difference 20

 9 10 19 20 29 30

Conclusion

82-42=40

The difference is 40

 4 5 14 15 24 25 34 35 44 45

The product of the number in the opposite corner of this rectangle is:

4x45=180

44x5=220

The difference between these products is:

220-180=40

Now i have found out that a rectangle sized 2 by 5 vertically is on anywhere in the 100 sqaure grid the difference is always going to be 40

From the 100-sqaure grids I will now choose a rectangle 2 by 6 vertically

 1 2 11 12 21 22 31 32 41 42 51 52

The product of the number in the opposite corner of this rectangle is:

1x52=52

51x2=102

The difference between these products is:

102-52=50

The difference is 50

 41 42 51 52 61 62 71 72 81 82 91 92

The product of the number in the opposite corner of this rectangle is:

41x92=3772

91x42=3822

The difference between these products is:

3822-3772=50

The difference is 50

 4 5 14 15 24 25 34 35 44 45 54 55

The product of the number in the opposite corner of this rectangle is:

4x55=220

54x5=270

The difference between these products is:

270-220=50

The difference is 50

Now I have found out that a rectangle sized 2 by 6 vertically is on anywhere in the 100 sqaure grid the difference is always going to be 50

Now I have found out that if i go up by 1 vertically (e.g. 2 by 7, 2 by 8, 2 by 9...) the answer will go up by 10.

Omar Ferdous 10a              -  -

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