we know that
If two lines are perpendicular, then the product o their slopes is equal to minus one
so
Step 1
<u>Find the slope of the given line</u>
we have
------->
This line is parallel to the y-axis
so
the perpendicular will be parallel to the x-axis
Step 2
The equation of the line perpendicular to the given line is the y-coordinate of the given point
Point
the equation is
therefore
<u>the answer is</u>
see the attached figure to better understand the problem
Let
x------> the length of the rectangle
y------> the width of the rectangle
we know that
The area of a rectangle is equal to
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
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
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
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
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
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
the dimensions of the rectangle are 60 units x 1 (1/15) units
see the draw in the attached figure N 6
