Question

Draw at least six different sized rectangles that have an area of 64 square units

Answer 1

Let

x------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of a rectangle is equal to

$A=x*y$

$A=64\ units^{2}$

so

$x*y=64$ --------> 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

$x*y=64$

$y=64/x$

$y=64/64$

$y=1\ units$      

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

$x*y=64$

$y=64/x$

$y=64/32$

$y=2\ units$

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

$x*y=64$

$y=64/x$

$y=64/16$

$y=4\ units$

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

$x*y=64$      

$y=64/x$

$y=64/30$

$y=\frac{32}{15} =2\frac{2}{15} \ units$

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

$x*y=64$    

$y=64/x$

$y=64/40$

$y=1.60\ units$

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

$x*y=64$    

$y=64/x$

$y=64/60$

$y=\frac{16}{15} =1\frac{1}{15} \ units$

the dimensions of the rectangle are 60 units x 1 (1/15) units

see the draw in the attached figure N 6