Opposite corner

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Opposite Corner

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

                                                                                                        

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

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

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8x20=160

18x10=180

The differences between these products are:

160-180=20

The difference is 20

 

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

81x93=7533

91x83=7553

The differences between these products are:

7533-7553=20

The difference is 20

Now i have found out that a rectangle sized 2 by 3 is on anywhere in the 100 sqaure grid the difference is always going to be 20

Now i am going to choose a rectangle from the 100-sqaure grid 2 by 3 horizontally

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