Mr.Jones needs to build a Rectangular 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 250ft. Which system of inequalities and graph represents the possible dimensions of the pen?
Let's say the length of the fence is x and the width of the fence is y.
According to the given conditions, we have the following inequalities:
1. The length of the fence should be at least 60 ft.
x ≥ 60
2. The distance around the fence should be no more than 250 ft.
2(x + y) ≤ 250
x + y ≤ 125
Now, let's plot the graph of these inequalities to represent the possible dimensions of the pen:
First, graph the inequality x ≥ 60:
- Draw a vertical line at x = 60.
Next, graph the inequality x + y ≤ 125:
- Rearrange the inequality to y ≤ 125 - x.
- Draw the line y = 125 - x, starting from the y-intercept (0, 125) and sloping downward.
Now, shade the region below the line y = 125 - x.
The shaded region represents the possible dimensions of the rectangular fence that Mr. Jones can build to keep his dog safe.