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.

Answer 1

Let
x------------> the length of the frame
y-----------> the width of the frame

we know that
Perimeter of the frame=2*(x+y)
2*(x+y) <=96
x>=(y-4)²

using a graph tool
see the attached figure

the solutions that are viable are those in which the values ​​of x and y are positive belonging to the total solution of the system

Answer 2

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