Ordered Pairs of points

Question

List four ordered pairs of points (l,w) that represent dimensions of rectangles with perimeters of 20 units.  

Answer 1

Just so I don't confuse anyone, I updated my answer up here too.........

 

 

OHHH now I see what the problem is asking for, its a little easier than what I was explaining (but the wording isn't the best).

It is essentially asking you to draw 4 different rectangles that have a perimeter of 20.

So for my example of 7 by 3, that would be 1 rectangle and you could write 7 in the L (length) column and 3 in the W (width) column. So this is a rectangle that has sides 3+7+3+7=20.

Another one could be a length of 1 and a width of 9 (1+9+1+9=20).

Just so I'm clear here is a set of solutions.

L W
1 9
2 8
3 7
4 6

Answer 2

L+W=10 is a straight line in the L-W plane all of whose points give the dimensions of such a rectangle.

There was no restriction to integral answers in the problem.

Answer 3

 Perimeter of rectangle  = 2L + 2W = 20

 

then   L+ w = 10

 

    Now have to think of all sets of 2 integers that add up to 10.

 

   If we write numbers from 1 to 10.

 

   1  2    3   4   5     6  7  8   9

 

   any 2 pairs first from left hand side from the 1st from right adds up to 10, because any successive number is 1 more than predecessor.

 

   so  1 + 9 = 10

        2 + 8 = 10

        3 + 7 = 10

        4 + 6 = 10

        5  + 5 = 10

        This problem becomes very important later in Algebra

        Where it says that what is maximum area that a farmer can cover with 20 meter of fence.

 

        It turns out that a square by each side 1/4 of perimeter covers maximum area, in this case  of 25

         square unit, which is greater area than any other rectangle made of other combinations.

  

        We can go further than this on other cases, that I am not going to do it now, that may cause

         confusion .

       It is good to see the relationship between numbers at this state.