Question

Edward is making a rectangular picture frame. He wants the perimeter of the frame to be no more than 96 inches. He also wants the length of the frame to be greater than or equal to the square of 4 inches less than its width.
Create a system of inequalities to model the above situation and use it to determine how many of the solutions are viable.

A.) Part of the solution region includes a negative length; therefore, all solutions are not viable for the given situation.

B.) No part of the solution region is viable because the length or width cannot be negative.

C.) The entire solution region is viable.

D.) Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.

Answer 1

Part I.
Let x represent the width of the frame, any y represent the length. The sum of length and width will be half the perimeter, so one inequality is
  x + y ≤ 48
If we assume the length restriction applies to the numeric values measured in inches, then the second inequality can be written as
  y ≥ (x-4)²

Part II.
The solution is shown in the figure where the colored regions overlap. Unless we also add restrictions x>0, y>0, some of the solution space is located where x < 0. Thus it is appropriate to conclude ...
  D.) Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.