Answer:
Part a)
[tex](x+y) > 35[/tex]
[tex]x \leq 30[/tex]
[tex]y \leq 20[/tex]
Part b) The graph in the attached figure
Part c) (30,20) and (25,15)
Step-by-step explanation:
Part a) write 3 constraints (inequalities) for this problem
Let
x -----> the length of the rectangle
y -----> the width of the rectangle
we know that
The perimeter of rectangle is
[tex]P=2(x+y)[/tex]
[tex]P > 70\ cm[/tex]
so
[tex]2(x+y) > 70[/tex] ---> the perimeter of a rectangle must be greater than 70 cm
Simplify
[tex](x+y) > 35[/tex] ----> inequality A
[tex]x \leq 30[/tex] ----> inequality B (the length cannot be greater than 30 cm)
[tex]y \leq 20[/tex] ----> inequality C (the width cannot be greater than 20 cm)
Part b) Graph all 3 constraints
we have
[tex](x+y) > 35[/tex]
[tex]x \leq 30[/tex]
[tex]y \leq 20[/tex]
using a graphing tool
The solution is the triangular shaded area
see the attached figure
Part c) what are two possible combinations for the length and width of the rectangle
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy all the inequalities of the system (The ordered pair must lie on the shaded area of the graph)
First possible combination
point (30,20) ----> the point lie on the shaded area
x=30 cm, y=20 cm
Verify if the ordered pair satisfy the inequalities
Inequality A
[tex](x+y) > 35[/tex]
[tex](30+20) > 35[/tex]
[tex](50) > 35[/tex] ----> is true
The ordered pair satisfy the inequality A
Inequality B
[tex]x \leq 30[/tex]
[tex]30 \leq 30[/tex] ---> is true
The ordered pair satisfy the inequality B
Inequality C
[tex]y \leq 20[/tex]
[tex]20 \leq 20[/tex] ----> is true
The ordered pair satisfy the inequality C
so
The ordered pair satisfy all the inequalities of the system
therefore
The ordered pair (30,20) is a possible combinations for the length and width of the rectangle
Second possible combination
point (25,15) ----> the point lie on the shaded area
x=25 cm, y=15 cm
Verify if the ordered pair satisfy the inequalities
Inequality A
[tex](x+y) > 35[/tex]
[tex](25+15) > 35[/tex]
[tex](40) > 35[/tex] ----> is true
The ordered pair satisfy the inequality A
Inequality B
[tex]x \leq 30[/tex]
[tex]25 \leq 30[/tex] ---> is true
The ordered pair satisfy the inequality B
Inequality C
[tex]y \leq 20[/tex]
[tex]15 \leq 20[/tex] ----> is true
The ordered pair satisfy the inequality C
so
The ordered pair satisfy all the inequalities of the system
therefore
The ordered pair (25,15) is a possible combinations for the length and width of the rectangle
