Answer:
The shortest side of the fence can have a maximum length of 80 feet
Step-by-step explanation:
Inequalities
To solve the problem, we use the following variables:
x=length of the longer side
y=length of the sorter side
The perimeter of a rectangle is calculated as:
P = 2x + 2y
The perimeter of the fence must be no larger than 500 feet. This condition can be written as:
[tex]2x + 2y \le 500[/tex]
The second condition states the longer side of the fence must be 10 feet more than twice the length of the shorter side.
This can be expressed as:
x = 10 + 2y
Substituting into the inequality:
[tex]2(10 + 2y) + 2y \le 500[/tex]
This is the inequality needed to determine the maximum length of the shorter side of the fence.
Operating:
[tex]20 + 4y + 2y \le 500[/tex]
Simplifying:
[tex]20 + 6y \le 500[/tex]
Subtracting 20:
[tex]6y \le 500 - 20[/tex]
[tex]6y \le 480[/tex]
Solving:
[tex]y \le 480 / 6[/tex]
[tex]y \le 80[/tex]
The shortest side of the fence can have a maximum length of 80 feet
