Let
x------> the length of the rectangle
y------> the width of the rectangle
we know that
The area of a rectangle is equal to
![A=64\ units^{2}](https://tex.z-dn.net/?f=A%3D64%5C%20units%5E%7B2%7D)
so
--------> equation 1
let's assume different values of x to get the different values of y
<u>case 1)</u> For x=64 units
substitute in the equation 1
![x*y=64](https://tex.z-dn.net/?f=x%2Ay%3D64)
![y=64/x](https://tex.z-dn.net/?f=y%3D64%2Fx)
![y=64/64](https://tex.z-dn.net/?f=y%3D64%2F64)
the dimensions of the rectangle are 64 units x 1 unit
see the draw in the attached figure N 1
<u>case 2)</u> For x=32 units
substitute in the equation 1
![x*y=64](https://tex.z-dn.net/?f=x%2Ay%3D64)
![y=64/x](https://tex.z-dn.net/?f=y%3D64%2Fx)
![y=64/32](https://tex.z-dn.net/?f=y%3D64%2F32)
![y=2\ units](https://tex.z-dn.net/?f=y%3D2%5C%20units)
the dimensions of the rectangle are 32 units x 2 units
see the draw in the attached figure N 2
<u>case 3)</u> For x=16 units
substitute in the equation 1
![x*y=64](https://tex.z-dn.net/?f=x%2Ay%3D64)
![y=64/x](https://tex.z-dn.net/?f=y%3D64%2Fx)
![y=64/16](https://tex.z-dn.net/?f=y%3D64%2F16)
![y=4\ units](https://tex.z-dn.net/?f=y%3D4%5C%20units)
the dimensions of the rectangle are 16 units x 4 units
see the draw in the attached figure N 3
<u>case 4)</u> For x=30 units
substitute in the equation 1
![y=64/x](https://tex.z-dn.net/?f=y%3D64%2Fx)
![y=64/30](https://tex.z-dn.net/?f=y%3D64%2F30)
![y=\frac{32}{15} =2\frac{2}{15} \ units](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B32%7D%7B15%7D%20%3D2%5Cfrac%7B2%7D%7B15%7D%20%5C%20units)
the dimensions of the rectangle are 30 units x 2 (2/15) units
see the draw in the attached figure N 4
<u>case 5)</u> For x=40 units
substitute in the equation 1
![y=64/x](https://tex.z-dn.net/?f=y%3D64%2Fx)
![y=64/40](https://tex.z-dn.net/?f=y%3D64%2F40)
![y=1.60\ units](https://tex.z-dn.net/?f=y%3D1.60%5C%20units)
the dimensions of the rectangle are 40 units x 1.60 units
see the draw in the attached figure N 5
<u>case 6)</u> For x=60 units
substitute in the equation 1
![y=64/x](https://tex.z-dn.net/?f=y%3D64%2Fx)
![y=64/60](https://tex.z-dn.net/?f=y%3D64%2F60)
![y=\frac{16}{15} =1\frac{1}{15} \ units](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B16%7D%7B15%7D%20%3D1%5Cfrac%7B1%7D%7B15%7D%20%5C%20units)
the dimensions of the rectangle are 60 units x 1 (1/15) units
see the draw in the attached figure N 6