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July 28, 2016
Posted by **Thelma** on Wednesday, April 9, 2014 at 9:02pm.

- math -
**Reiny**, Wednesday, April 9, 2014 at 9:45pmlet the dimensions of the first plot be x by y

let the dimensions of the second plot be a by b

where x,y, a, and b are all integers.

so we want:

xy + ab = 60, and

x-y = a+b

There are many combinations that will work

e.g.

15 2 30 3 10 30

x=15

y=2

a=3

b=10

area of first = 30, area of 2nd = 30, total = 60

difference of 1st dimensions = 15-2 = 13

sum of 2nd dimensions = 3+10 = 13

I ran a simple 1980's type of "BASIC" program and got the following:

my columns are :

thex, the y, the first area, the a , the b, the area of the 2nd.

you can check any one of them , they all work

10 for x = 1 to 60

20 for y = 1 to 60

30 for a = 1 to 60

40 for b = 1 to 60

50 if (x*y+a*b) = 60 then goto 60 else goto 200

60 if (x-y) = (a+b) then print x,y,x*y,a,b,a*b

200 next b

210 next a

220 next y

230 next x

>run

11 5 55 1 5 5

11 5 55 5 1 5

12 4 48 2 6 12

12 4 48 6 2 12

13 3 39 3 7 21

13 3 39 7 3 21

13 4 52 1 8 8

13 4 52 8 1 8

14 2 28 4 8 32

14 2 28 8 4 32

14 3 42 2 9 18

14 3 42 9 2 18

15 1 15 5 9 45

15 1 15 9 5 45

15 2 30 3 10 30

15 2 30 10 3 30

16 1 16 4 11 44

16 1 16 11 4 44

16 3 48 1 12 12

16 3 48 12 1 12

17 2 34 2 13 26

17 2 34 13 2 26

18 1 18 3 14 42

18 1 18 14 3 42

21 2 42 1 18 18

21 2 42 18 1 18

22 1 22 2 19 38

22 1 22 19 2 38

31 1 31 1 29 29

31 1 31 29 1 29