Mr. Jones needs to build a fence in his backyard to keep their dog safe. The length of the fence should be at least 60 ft, and the distance around should be no more than 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen?
Responses
Let's suppose the length of the fence is represented by x and the width of the fence is represented by y.
Given that the length should be at least 60 ft, we have the inequality x ≥ 60.
Also, the distance around should be no more than 260 ft, meaning the perimeter of the fence should be less than or equal to 260 ft. The perimeter is given by the equation: 2x + 2y ≤ 260.
Therefore, the system of inequalities representing the possible dimensions of the pen is:
x ≥ 60
2x + 2y ≤ 260
To graph this system of inequalities, plot the horizontal line x = 60 (since x should be greater than or equal to 60), and then shade the region below the line. Then, plot the line 2x + 2y = 260 (which can be rewritten as y ≤ 130 - x), and shade the region below that line. The shaded region where the two shaded regions intersect will represent the possible dimensions of the pen.
https://www.desmos.com/calculator/tzjkqj0ztx