Two rectangular garden plots with an area of 60 square feet have distinct integer dimensions. The difference in the dimensions of one plot is the same as the sum of the dimensions of the other plot. what are the dimensions of the 2 garden plots?

Answer 1

let 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