Question

Draw a rectangle that has a area of a square Units and a perimeter of 12 units what are the side length of the rectangle

Answer 1

Let s represent the length of one side of this rectangle, and w represent the width of the rectangle (length of one end).  Then 2s + 2w = 12 units, and the area is a = s*w.  Using the previous equation we can eliminate either s or w.  Since we want s, eliminate w:  2w = 12 - 2s, or w = 6 - s.

Then the area of the rect. is a = s(6 - s) = 6s - s^2.

You have not shared the actual area of the rect., but have represented it by "a."

Suppose that the area is given and is 90.  Then 90 square units = 6s - s^2, so that -s^2 + 6s - 90 = 0.  Using the Pyth. Thm., we find s as follows:

       -6 plus or minus sqrt( 6^2 - 4(-1)(-90)
s = ---------------------------------------------------
                            2(-1)

Unfortunately, s would come out as a pair of complex numbers, which is not possible in a situation where you're calculating lengths.

Please recheck this problem.  Was the aera of the rectangle, a, given?