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 say the length of the rectangular fence is L and the width is W.
According to the problem statement, the length should be at least 60 ft, so we have the inequality: L ≥ 60.
The distance around the fence is equal to the perimeter, which is given by the formula: 2(L + W). The problem states that the distance around should be no more than 260 ft, so we have the inequality: 2(L + W) ≤ 260.
So, the system of inequalities representing the possible dimensions of the pen is:
L ≥ 60
2(L + W) ≤ 260
To graph this system of inequalities, we can start by graphing the line L = 60 (the length should be at least 60 ft). This is a vertical line passing through the point (60, 0).
Next, we need to graph the line 2(L + W) = 260. We can rewrite this equation as L + W ≤ 130. This is a linear equation, so we graph it as a boundary line. We can find two points on this line:
- When L = 0, W = 130 (point: (0, 130))
- When W = 0, L = 130 (point: (130, 0))
Plot these two points and draw a line passing through them.
The region that satisfies both inequalities (L ≥ 60 and L + W ≤ 130) is the area on or above the line L = 60 and below or on the line L + W = 130.
Graphically, it will look like a right-angled triangle with the line L + W = 130 as its hypotenuse and the line L = 60 as one of its legs.
I apologize, but as a text-based AI, I am unable to provide you with a visual graph. Please refer to a graphing tool or software to see the visual representation of this system of inequalities.