Let
x------> the length of the rectangle
y------> the width of the rectangle
we know that
The area of a rectangle is equal to
[tex]A=x*y[/tex]
[tex]A=64\ units^{2}[/tex]
so
[tex]x*y=64[/tex] --------> equation 1
let's assume different values of x to get the different values of y
case 1) For x=64 units
substitute in the equation 1
[tex]x*y=64[/tex]
[tex]y=64/x[/tex]
[tex]y=64/64[/tex]
[tex]y=1\ units[/tex]
the dimensions of the rectangle are 64 units x 1 unit
see the draw in the attached figure N 1
case 2) For x=32 units
substitute in the equation 1
[tex]x*y=64[/tex]
[tex]y=64/x[/tex]
[tex]y=64/32[/tex]
[tex]y=2\ units[/tex]
the dimensions of the rectangle are 32 units x 2 units
see the draw in the attached figure N 2
case 3) For x=16 units
substitute in the equation 1
[tex]x*y=64[/tex]
[tex]y=64/x[/tex]
[tex]y=64/16[/tex]
[tex]y=4\ units[/tex]
the dimensions of the rectangle are 16 units x 4 units
see the draw in the attached figure N 3
case 4) For x=30 units
substitute in the equation 1
[tex]x*y=64[/tex]
[tex]y=64/x[/tex]
[tex]y=64/30[/tex]
[tex]y=\frac{32}{15} =2\frac{2}{15} \ units[/tex]
the dimensions of the rectangle are 30 units x 2 (2/15) units
see the draw in the attached figure N 4
case 5) For x=40 units
substitute in the equation 1
[tex]x*y=64[/tex]
[tex]y=64/x[/tex]
[tex]y=64/40[/tex]
[tex]y=1.60\ units[/tex]
the dimensions of the rectangle are 40 units x 1.60 units
see the draw in the attached figure N 5
case 6) For x=60 units
substitute in the equation 1
[tex]x*y=64[/tex]
[tex]y=64/x[/tex]
[tex]y=64/60[/tex]
[tex]y=\frac{16}{15} =1\frac{1}{15} \ units[/tex]
the dimensions of the rectangle are 60 units x 1 (1/15) units
see the draw in the attached figure N 6
