Opposite Corners (Maths)

Ok since it's the holiday i can't exactly go to a teacher for advice so I thought the next best thing was to query here.

Opposite corners; this is where for example on a 10 x 10 grid you select a small square (e.g. 2 x 2) then work out the difference for a variety of squares until you come up with a rule algebraically.

I have found the rule for squares which is (n-1)² x 10 (n being the small you want to find and 10 being the size grid you are using) so I can now find any difference of any small square and any size grid.

That was worked out as i plotted the results into a table as shown below:

Size of Small Square | Difference
2 x 2 10 1 x 10 1² x 10
3 x 3 40 4 x 10 2² x 10
4 x 4 90 9 x 10 3² x 10

Then noticed that the third column are all square numbers.

I then had to go on to look at rectangles to look find a rule as well but I am struggling to do so. I have used a variety of rectangles on a 10 x 10 scale and plotted them into a table as shown below:

Size of Small Square Difference
2 x 3 20
2 x 4 30
3 x 4 60
4 x 5 120

Although now i'm confused because I work out anything from here :confused:

Can somebody help me please :frown:

It's coming to desperate measures!

Reply 1

GH

13

AHH, I still remember this coursework. Just keep at it, and play around with the algebra. After an hour or so, the formulae should fall out easily enough

Reply 2

john !!

14

yep, same here. you can do it with a square (or we did them with an infinite number of rows and a set number of columns)

there are all formulas for the area of a rectangle, and even for a varying number of columns.

Reply 3

siliviax

OP

ok i have found out the rule for 10 x 10 squares for rectangles.. which is 10(L-1)(w-1)

Although i didn't know how i came to this conclusion and i was wondering if you could give me some advice :frown:

needs to be handed in on monday.

i found these out:

size - - difference
2 x 3 - - 20
2 x 4 - - 30
3 x 4 - - 60
4 x 5 - - 120

and that 2 x 3 = same difference as 3 x 2 etc

any help would be very nice!

Reply 4

siliviax

OP

help would be nice :smile:

xx

Reply 5

siliviax

OP

please, i have till monday morning to do it! :frown:

Reply 6

IntegralAnomaly

siliviax

ok i have found out the rule for 10 x 10 squares for rectangles.. which is 10(L-1)(w-1)

Although i didn't know how i came to this conclusion and i was wondering if you could give me some advice :frown:

needs to be handed in on monday.

i found these out:

size - - difference
2 x 3 - - 20
2 x 4 - - 30
3 x 4 - - 60
4 x 5 - - 120

and that 2 x 3 = same difference as 3 x 2 etc

any help would be very nice!

i don't understand what ur asking,u'v proved the formula!!
eg 10(2-1)(3-1)=20

Reply 7

siliviax

OP

i know but i need to show how i came to that conclusion, any help?

Opposite Corners (Maths)

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