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 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen?
Let's denote the length of the fence as L and the width of the fence as W.
From the given information, we have two inequalities:
1) The length of the fence should be at least 60 ft: L ≥ 60
2) The distance around (perimeter) should be no more than 260 ft: 2L + 2W ≤ 260
To graph these inequalities, we can plot L on the x-axis and W on the y-axis. Let's start with the first inequality:
1) L ≥ 60:
This means that the length L should be greater than or equal to 60. Graphically, this is represented by a dashed line parallel to the x-axis passing through the point (60, 0) because L can take any value greater than or equal to 60.
We shade the region to the right of the line to represent L ≥ 60.
Next, let's graph the second inequality:
2) 2L + 2W ≤ 260:
To make it easier to graph, let's divide this inequality by 2:
L + W ≤ 130
To graph this inequality, let's rewrite it as:
W ≤ 130 - L
This represents a straight line when W = 130 - L, passing through the points (0, 130) and (130, 0).
We shade the region below this line to represent W ≤ 130 - L.
The possible dimensions of the pen are the values of L and W that satisfy both inequalities, i.e., the region where the two shaded regions overlap.
The graph of the system of inequalities will show this region. Unfortunately, I am unable to draw the graph since I can only provide a textual response. However, you can plot the equations on a graph using any graphing tool to see the possible dimensions of the pen.